Adam Osękowski

Professor, Institute of Mathematics, University of Warsaw

Summary

1. Home
2. Publications
3. Teaching

Books

• A. Osękowski, Sharp martingale and semimartingale inequalities, Monografie Matematyczne 72 (2012), Birkhäuser, 462 pp.
• I. Pinelis, V. de la Pena, R. Ibragimov, A. Osękowski, I. Shevtsova, Inequalities and Extremal Problems in Probability and Statistics: Selected Topics, Academic Press, Elsevier, 2017, 200 pp.

Publications

2024

• T. Gałązka, Y. Jiao, A. Osękowski, Lian Wu The sharp weighted maximal inequalities for noncommutative martingales, Journal of Functional Analysis 286 (2024), Paper no. 110270, 41. (original pdf)
• A. Osękowski, A sharp two-weight estimate for the maximal operator under a bump condition, Monatshefte fur Mathematik 203 (2024), pp. 653--665. (original pdf)
• S. Cichomski, A. Osękowski, Coherent distributions on the square–extreme points and asymptotics, Journal of Applied Probability 61 (2024), pp. 1240--1262. (original pdf)
• S. Cichomski, A. Osękowski, Contradictory predictions with multiple agents, ALEA. Latin American Journal of Probability and Mathematical Statistics 21 (2024), pp. 369--383. (original pdf)
• A. Osękowski, Weighted estimates for the multilinear maximal operator, Collectanea Mathematica 75 (2024), pp. 379--394. (original pdf)
• A. Osękowski, A sharp Lp estimate for the total variation process, Statistics and Probability Letters 206 (2024), paper no. 109997, 5. (original pdf)
• A. Małek, A. Osękowski, A noncommutative Freedman inequality, Electronic Communications in Probability 29 (2024), paper no. 43, 11. (original pdf)
• T. Gałązka, A. Osękowski, Sharp L^p → L^q,∞ estimates for the Hilbert transform, Journal of the Mathematical Society of Japan 76 (2024), pp. 111--124. (original pdf)
• M. Akboudj, Y. Jiao, A. Osękowski, Non-symmetric differentially subordinate martingales and sharp weak-type bounds for Fourier multipliers, Science China. Mathematics 67 (2024), 1807--1826. (original pdf)
• E. Bednarz, P. Ernst and A. Osękowski, On the diameter of the stopped spider process, Mathematics of Operations Research 49 (2024), pp. 346--365. (original pdf)

2023

• T. Gałązka, A. Osękowski, Sharp estimates for martingale transforms with unbounded transforming sequences, Electronic Journal of Probability 28 (2023), paper no. 66. (original pdf)
• S. Cichomski, A. Osękowski, Doob's estimate for coherent random variables and maximal operators on trees, Probability and Mathematical Statistics 43 (2023), 109--119. (original pdf)
• A. Osękowski, BLO class under the change of measure, The Tohoku Mathematical Journal 75 (2023), 161--173. (original pdf)
• Ł. Kamiński, A. Osękowski, On the best constant in the L^p estimate for the sharp maximal function, Journal of Mathematical Analysis and Applications 518 (2023), Paper No. 126733. (original pdf)

2022

• Y. Jiao, A. Osękowski, L. Wu, Y. Zuo, Inequalities for noncommutative weakly dominated martingales and applications, Communications in Mathematical Physics 396 (2022), pp. 787--816. (original pdf)
• T. Gałązka, A. Osękowski, A probabilistic approach to Hilbert transforms on free group von Neumann algebras, Proceedings of the American Mathematical Society 150 (2022), pp. 2861--2877. (original pdf)
• A. Osękowski, M. Rapicki, Sharp weighted inequalities for harmonic maximal operators, New York Journal of Mathematics 28 (2022), pp. 140--153. (original pdf)
• A. Osękowski, M. Wojtas, Weak-type estimates for martingale maximal functions, Electronic Communications in Probability 27 (2022), paper no. 52. (original pdf)
• A. Osękowski, Sharp L^p estimates for paraproducts on general measure spaces, Archiv der Mathematik 118 (2022), 91--99. (original pdf)

2021

• A. Osękowski, I. Yaroslavtsev, The Hilbert transform and orthogonal martingales in Banach spaces, International Mathematics Research Notices 15 (2021), 11670--11730. (original pdf)
• A. Osękowski, Sharp Lorentz-norm estimates for differentially subordinate martingales and applications, Transactions of the American Mathematical Society 374 (2021), 7235--7262. (original pdf)
• A. Osękowski, The dual conjecture of Muckenhoupt and Wheeden, Revista Matemàtica Iberoamericana 37 (2021), 2285--2308. (original pdf)
• R. Bañuelos, T. Gałązka, A. Osękowski, A dual approach to Burkholder's L^p estimates, Bulletin of the London Mathematical Society 53 (2021), 1107--1123. (original pdf)
• Ł. Kamiński, A. Osękowski, An extension of a Hardy's inequality and its applications, Mathematical Inequalities and Applications 24 (2021), 679--694. (original pdf)
• S. Cichomski and A. Osękowski, The Maximal Difference Among Experts' Opinions, Electronic Journal in Probability 26 (2021), pp. 1–17. (original pdf)
• A. Osękowski, Explicit counterexamples to the weak Muckenhoupt-Wheeden conjecture, Mathematische Zeitschrift 298 (2021), pp. 1727--1734. (original pdf)
• T. Gałązka, A. Osękowski, Weighted inequalities for q-functions, Illinois Journal of Mathematics 65 (2021), pp. 455–-474. (original pdf)
• M. Brzozowski, A. Osękowski, Weighted maximal inequalities for martingale transforms, Probability and Mathematical Statistics 41 (2021), pp. 89--114. (original pdf)
• A. Osękowski, An extension of Pratelli's inequality, Statistics and Probability Letters 177 (2021), Paper No. 109175. (original pdf)
• A. Osękowski, Best constants in weighted estimates for dyadic shifts, Integral Equations Operator Theory 93 (2021), Paper No. 4, 18 pp. (original pdf)
• A. Osękowski, Sharp weak-type (p, p) estimates (1 < p < ∞) for positive dyadic shifts, Mediterranean Journal of Mathematics 18 (2021), Paper No. 44, 17 pp. (original pdf)
• A. Osękowski, Y. Zuo, Sharp maximal L^p-bounds for continuous martingales and their differential subordinates, Electronic Journal in Probability 26 (2021), pp. 1–22. (original pdf)
• Ł. Kamiński, A. Osękowski, Sharp Lorentz-norm estimates for BMO martingales, Statistics and Probability Letters 173 (2021), 109068. (original pdf)
• A. Osękowski, M. Rapicki, Sharp Lorentz-norm estimates for dyadic-like maximal operators, Studia Mathematica 257 (2021), pp. 87-–110. (original pdf)
• T. Gałązka, A. Osękowski and Y. Zuo, A weak-type (∞,∞) inequality for the triangular projection, Linear Algebra and its Applications 612 (2021), pp. 112–127. (original pdf)
• Ł. Kamiński, A. Osękowski, Best constants in some estimates for the harmonic maximal operator on the real line, Colloquium Mathematicum 164 (2021), pp. 133–148. (original pdf)
• A. Osękowski, M. Rapicki, A weighted maximal weak-type inequality, Mathematika 67 (2021), pp. 145–157. (original pdf)
• A. Osękowski, Embedding BMO into weighted BMO, Publicacions Matemàtiques 65 (2021), pp. 335–361. (original pdf)
• M. Akboudj, Y. Jiao, A. Osękowski, A weak-L^∞ inequality for weakly dominated martingales with applications to Haar shift operators, Journal of Mathematical Analysis and Applications 493 (2021), pp. 124547. (original pdf)
• A. Osękowski, On the best constant in the estimate related to H¹-BMO duality, Proceedings of the American Mathematical Society 149 (2021), pp. 333–343. (original pdf)

2020

• R. Bañuelos, M. Brzozowski, A. Osękowski, Burkholder's function and a weighted L² bound for stochastic integrals, Proceedings of the American Mathematical Society 148 (2020), pp. 5013-–5028. (original pdf)
• A. Osękowski, On A_p-A_q weighted estimates for maximal operators, Annales Academiae Scientiarum Fennicae Mathematica 45 (2020), pp. 1171–1185. (original pdf)
• A. Osękowski, Inequalities for second-order Riesz transforms associated with Bessel expansion, Bulletin of the Polish Academy of Sciences Mathematics 68 (2020), pp. 75--88. (original pdf)
• A. Osękowski, On the best constant in the martingale version of Fefferman's inequality, Bernoulli 26 (2020), pp. 1912--1926. (original pdf)
• A. Osękowski, A note on H¹ - BMO duality, Archiv der Mathematik 114 (2020), pp. 687--697. (original pdf)
• A. Osękowski, A ratio inequality for nonnegative martingales and their differential subordinates, Electronic Communications in Probability 25 (2020), paper no. 21, pp. 1--12. (original pdf)
• M. Akboudj, Y. Jiao, A. Osękowski, Weak-L^∞ inequality for non-symmetric martingale transforms and Haar system, Statistics and Probability Letters 163 (2020), 108778. (original pdf)
• A. Osękowski, Weighted weak-type inequalities for square functions, Mathematical Inequalities and Applications 23 (2020), pp. 267--286. (original pdf)

2019

• Y. Jiao, A. Osękowski, L. Wu, Strong differential subordinates for noncommutative submartingales, Annals of Probability 47 (2019), pp. 3108--3142. (original pdf)
• A. Osękowski, On the action of the Hilbert transform on l₁^N-valued functions, Statistics and Probability Letters 146 (2019), pp. 213--223. (original pdf)
• A. Osękowski, A sharp estimate for Muckenhoupt class A_∞ and BMO, Positivity 23 (2019), pp. 711--725. (original pdf)
• M. Brzozowski, A. Osękowski, Sharp weighted weak type (∞,∞) inequality for differentially subordinate martingales, Statistics and Probability Letters 62 (2019), pp. 108561.
• A. Osękowski, L. Slavin, V. Vasyunin, The maximal operator from BMO to BLO on alpha-trees (in Russian), Algebra i Analiz 31 (2019), pp. 106--153. (original pdf)

2018

• R. Bañuelos, A. Osękowski, Stability in Burkholder's differentially subordinate martingale inequalities and applications to Fourier multipliers, Journal de Mathématiques Pures et Appliquées 119 (2018), pp. 1--44. (original pdf)
• Y. Jiao, A. Osękowski, L. Wu, Inequalities for noncommutative differentially subordinate martingales, Advances in Mathematics 337 (2018), pp. 216--259. (original pdf)
• K. Domelevo, A. Osękowski, S. Petermichl, Various sharp estimates for semi-discrete Riesz transforms of the second order, Operator Theory: Advances and Applications 261 (2018), pp. 229--255. (original pdf)
• A. Osękowski, A weighted weak-type bound for Haar multipliers, The Royal Society of Edinburgh Proceedings A (Mathematics) 148A (2018), pp. 643--658. (original pdf)
• A. Osękowski, Square function inequalities for monotone bases in L¹, Banach Journal of Mathematical Analysis 12 (2018), pp. 693--708. (original pdf)
• A. Osękowski, Weighted maximal inequalities for the Haar system, Monatshefte für Mathematik 186 (2018), pp. 321--336. (original pdf)
• R. Bañuelos, A. Osękowski, Sharp Weighted L² inequalities for square functions, Transactions of the American Mathematical Society 370 (2018), pp. 2391--2422. (original pdf)
• R. Bañuelos, A. Osękowski, A weighted maximal inequality for differentially subordinate martingales, Proceedings of the American Mathematical Society 146 (2018), pp. 2277--2281. (original pdf)
• A. Osękowski, Sharp Lp-bounds for the martingale maximal function, Tohoku Mathematical Journal 70 (2018), pp. 121--138. (original pdf)
• A. Osękowski, Sharp logarithmic estimates for positive dyadic shifts, Advances in Mathematics 324 (2018), pp. 118--147. (original pdf)
• A. Osękowski, Weighted square function inequalities, Publicacions Matemàtiques 62 (2018), pp. 75--94. (original pdf)

2017

• A. Osękowski, Best constants in Muckenhoupt's inequality, Annales Academiae Scientiarum Fennicae Mathematica 42 (2017), pp. 889--904. (original pdf)
• A. Osękowski, Sharp LlogL estimates for Fourier multipliers, The Quarterly Journal of Mathematics 68 (2017), pp. 1357--1377. (original pdf)
• A. Osękowski, A Fefferman-Stein inequality for the martingale square and maximal functions, Statistics and Probability Letters 129 (2017), pp. 81--85. (original pdf)
• A. Osękowski, Weighted weak-type inequality for martingales, Bulletin of the Polish Academy of Sciences Mathematics 65 (2017), pp. 165--175. (original pdf)
• A. Osękowski, Two-weight inequalities for geometric maximal operators, Mathematical Inequalities and Applications 20 (2017), pp. 1121--1138. (original pdf)
• A. Osękowski, Sharp weighted bounds for geometric maximal operators, Glasgow Mathematical Journal 59 (2017), pp. 533--547. (original pdf)
• M. Brzozowski, A. Osękowski, M. Rapicki, Sharp weighted weak-norm estimates for maximal functions, Statistics and Probability Letters 131 (2017), pp. 93--101. (original pdf)
• A. Osękowski, Weighted inequalities for martingale transforms and stochastic integrals, Mathematika 63 (2017), pp. 433--450. (original pdf)
• A. Osękowski, Inequalities for Hilbert operator and its extensions: the probabilistic approach, Annals of Probability 45 (2017), pp. 535--563. (original pdf)
• R. Bañuelos, A. Osękowski, Sharp weak type inequalities for fractional integral operators, Potential Analysis 47 (2017), pp. 103--121. (original pdf)
• T. Bekjan, Z. Chen, A. Osękowski, Noncommutative maximal inequalities associated with convex functions, Transactions of the American Mathematical Society 369 (2017), pp. 409--427. (original pdf)
• A. Osękowski, Weighted inequalities for the martingale square and maximal functions, Statistics and Probability Letters 120 (2017), pp. 95--100. (original pdf)

2016

• A. Osękowski, A sharp weak-type (∞,∞) inequality for the Hilbert transform, Complex Analysis and Operator Theory 10 (2016), pp. 1133--1143. (original pdf)
• A. Osękowski, Sharp weighted logarithmic bound for maximal operators, Archiv der Mathematik 107 (2016), pp. 635--644. (original pdf)
• A. Osękowski, Weighted Inequalities for the Dyadic Square Function, Integral Equations and Operator Theory 85 (2016), pp. 359--380. (original pdf)
• A. Osękowski, Sharp inequalities for the Haar system and martingale transforms, Probability and Mathematical Statistics 36 (2016), pp. 147--164. (original pdf)
• A. Osękowski, Sharp inequalities for monotone bases in L¹, Houston Journal of Mathematics 42 (2016), pp. 833--851. (original pdf)
• A. Osękowski, Weighted maximal inequality for differentially subordinate martingales, Electronic Communications in Probability 21 (2016), paper no. 23, pp. 1--10. (original pdf)
• A. Osękowski, On Carlson-Levin inequalities, Analysis Mathematica 42 (2016), pp. 55--67. (original pdf)
• A. Osękowski, Sharp estimates for Lipschitz class, The Journal of Geometric Analysis 26 (2016), pp. 1346--1369. (original pdf)
• A. Osękowski, Sharp Lp bound for holomorphic functions on the unit disc, Mediterranean Journal of Mathematics 13 (2016), pp. 127--139. (original pdf)
• A. Osękowski, Sharp logarithmic inequalities for Hardy operators, Zeitschrift für Analysis und ihre Anwendungen (Journal of Analysis and its Applications) 35 (2016), pp. 1--20. (original pdf)
• A. Osękowski, On the UMD constant of the space l₁^N, Colloquium Mathematicum 142 (2016), pp. 135--147. (original pdf)
• A. Osękowski, A logarithmic bound for a stopped Brownian motion, Stochastic Analysis and Applications 34 (2016), pp. 65--74. (original pdf)

2015

• A. Osękowski, Sharp maximal estimates for BMO martingales, Osaka Journal of Mathematics 52 (2015), pp. 1125--1143. (original pdf)
• R. Bañuelos, A. Osękowski, Weighted norm inequalities for fractional maximal operators - a Bellman function approach, Indiana University Mathematics Journal 64 (2015), pp. 957--972. (original pdf)
• R. Bañuelos, A. Osękowski, On Astala’s theorem for martingales and Fourier multipliers, Advances in Mathematics 283 (2015), pp. 275--302. (original pdf)
• R. Bañuelos, A. Osękowski, Sharp martingale inequalities and applications to Riesz transforms on manifolds, Lie groups and Gauss space, Journal of Functional Analysis 269 (2015), pp. 1652--1713. (original pdf)
• A. Osękowski, Sharp weak-type estimates for the dyadic-like maximal operators, Taiwanese Journal of Mathematics 19 (2015), pp. 1031--1050. (original pdf)
• A. Osękowski, Sharp inequalities for Hilbert transform in a vector-valued setting, Mathematical Inequalities and Applications 18 (2015), pp. 1561--1573. (original pdf)
• A. Osękowski, Weak-L^∞ inequalities for BMO functions, New York Journal of Mathematics 21 (2015), pp. 699--713. (original pdf)
• A. Osękowski, Sharp logarithmic inequalities for two Hardy-type operators, Bulletin of the Polish Academy of Sciences Mathematics 63 (2015), pp. 237--247. (original pdf)
• A. Osękowski, A weak type inequality for submartingales and Itô processes, Bulletin of the Polish Academy of Sciences Mathematics 63 (2015), pp. 73--88. (original pdf)
• A. Osękowski, Kolmogorov's inequalities for martingales and the Haar system, Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie 58 (2015), pp. 181--192. (original pdf)
• A. Osękowski, A sharp maximal inequality for one-dimensional Dunkl martingales, Statistics and Probability Letters 105 (2015), pp. 114--110. (original pdf)
• A. Osękowski, A prophet inequality for L^p-bounded dependent random variables, Positivity 19 (2015), pp. 289--303. (original pdf)
• A. Osękowski, Sharp L¹(l^q) estimate for a sequence and its predictable projection, Statistics and Probability Letters 104 (2015), pp. 82--86. (original pdf)
• A. Osękowski, Estimates for the diameter of a martingale, Stochastics: An International Journal of Probability and Stochastic Processes 87 (2015), pp. 235--256. (original pdf)
• A. Osękowski, Weighted weak-type inequalities for some fractional integral operators, Proceedings of the Japan Academy, Series A 91 (2015), pp. 35--38. (original pdf)
• A. Osękowski, Sharp estimates for holomorphic functions on the unit ball of ℂⁿ, Complex Variables and Elliptic Equations 60 (2015), pp. 323--332. (original pdf)
• A. Osękowski, A splitting procedure for Bellman functions and the action of dyadic maximal operators on L^p, Mathematika 61 (2015), pp. 199--212. (original pdf)
• A. Osękowski, A new approach to Hardy-type inequalities, Archiv der Mathematik 104 (2015), pp. 165-176. (original pdf)
• A. Osękowski, Sharp inequalities for BMO functions, Chinese Annals of Mathematics, Series B 36 (2015), pp. 225--236. (original pdf)

2014

• R. Bañuelos, A. Osękowski, On the Bellman function of Nazarov, Treil and Volberg, Mathematische Zeitschrift 278 (2014), pp. 385--399. (original pdf)
• R. Bañuelos, A. Osękowski, Sharp maximal L^p-estimates for martingales, Illinois Journal of Mathematics 58 (2014), pp. 149--165. (original pdf)
• A. Osękowski, Sharp L^p,∞ → L^q estimates for the dyadic-like maximal operators, Journal of Fourier Analysis and Applications 20 (2014), pp. 911--933. (original pdf)
• A. Osękowski, Sharp localized inequalities for Fourier multipliers, Canadian Journal of Mathematics 66 (2014), pp. 1358--1381. (original pdf)
• A. Osękowski, Some sharp estimates for the Haar system and other bases in L^1(0,1), Mathematica Scandinavica 115 (2014), pp. 123--142. (original pdf)
• A. Osękowski, Functional equations and sharp weak-type inequalities for the martingale square function, Mathematical Inequalities and Applications 17 (2014), pp. 1499--1513. (original pdf)
• A. Osękowski, A weak-type inequality for the martingale square function, Statistics and Probability Letters 95 (2014), pp. 139--143. (original pdf)
• A. Osękowski, Weak type inequalities for Fourier multipliers with applications to Beurling-Ahlfors transform, Journal of the Mathematical Society of Japan 66 (2014), pp. 745--764. (original pdf)
• A. Osękowski, On restricted weak-type constants of Fourier multipliers, Publicacions Matemàtiques 58 (2014), pp. 415--443. (original pdf)
• A. Osękowski, Sharp Weak-Type Inequality for the Haar System, Harmonic Functions and Martingales, Bulletin of the Polish Academy of Sciences Mathematics 62 (2014), pp. 187--196. (original pdf)
• A. Osękowski, Maximal inequalities for functions of bounded lower oscillation, Kyushu Journal of Mathematics, 68 (2014), pp. 297--305. (original pdf)
• A. Osękowski, Sharp L²log L inequalities for the Haar system and martingale transforms, Statistics and Probability Letters, 94 (2014), pp. 91--97. (original pdf)
• A. Osękowski, Weak-type inequalities for maximal operators acting on Lorentz spaces, Calculus of Variations and PDEs, Banach Center Publications 101 (2014), pp. 145--162. (original pdf)
• A. Osękowski, On the action of Riesz transforms on the class of bounded functions, Complex Analysis and Operator Theory 8 (2014), pp. 1269--1283. (original pdf)
• A. Osękowski, Sharp inequalities for Riesz transforms, Studia Mathematica 222 (2014), pp. 1-18. (original pdf)
• A. Osękowski, Sharp weak type estimates for Riesz transforms, Monatshefte für Mathematik 174 (2014), pp. 305--327. (original pdf)
• A. Osękowski, Maximal weak-type inequality for stochastic integrals, Electronic Communications in Probability 19 (2014), Article 25, pp. 1--13. (original pdf)
• A. Osękowski, Sharp weak-type inequalities for Fourier multipliers and second-order Riesz transforms, Central European Journal of Mathematics 12 (2014), pp. 1198--1213. (original pdf)
• R. Bañuelos, A. Osękowski, On the operator Λ* and the Beurling-Ahlfors transform on radial functions, Michigan Mathematical Journal 63 (2014), pp. 213--221. (original pdf)
• A. Osękowski, Maximal inequalities for martingales and their differential subordinates, Journal of Theoretical Probability 27 (2014), pp. 1--21. (original pdf)
• A. Osękowski, Sharp Weak Type Inequality for Fractional Integral Operators Associated with d-Dimensional Walsh-Fourier Series, Integral Equations and Operator Theory 78 (2014), pp. 589--600. (original pdf)
• A. Osękowski, Inequalities for the truncated Hilbert transform and the segment multiplier, Collectanea Mathematica 65 (2014), pp. 103--118. (original pdf)
• A. Osękowski, Inequalities for martingales taking values in 2-convex Banach spaces, Statistics and Probability Letters 84 (2014), pp. 102--107. (original pdf)

2013

• R. Bañuelos, A. Osękowski, Sharp inequalities for the Beurling-Ahlfors transform on radial functions, Duke Mathematical Journal 162 (2013), pp. 417--434.
• R. Bañuelos, A. Osękowski, Burkholder inequalities for submartingales, Bessel processes and conformal martingales, American Journal of Mathematics 135 (2013), pp. 1675--1698.
• A. Osękowski, Survey article: Bellman function method and sharp inequalities for martingales, Rocky Mountain Journal of Mathematics 43 (2013), pp. 1759--1823. (original pdf)
• A. Osękowski, Logarithmic inequalities for Fourier multipliers, Mathematische Zeitschrift 274 (2013), pp. 515--530. (original pdf)
• A. Osękowski, Sharp inequalities for martingales with values in \ell_\infty^N, Electronic Journal of Probability 18 (2013) no. 73, pp. 1--19. (original pdf)
• A. Osękowski, A sharp logarithmic bound for Beurling-Ahlfors operator restricted to the class of radial functions, Mediterranean Journal of Mathematics 10 (2013), pp. 1883--1894. (original pdf)
• A. Osękowski, Maximal Weak-Type Inequality for Orthogonal Harmonic Functions and Martingales, Bulletin of the Polish Academy of Sciences Mathematics 61 (2013), pp. 209--218. (original pdf)
• A. Osękowski, Moment inequality for the martingale square function, Bulletin of the Polish Academy of Sciences Mathematics 61 (2013), pp. 169--180. (original pdf)
• A. Osękowski, Weighted maximal inequalities for martingales, Tohoku Mathematical Journal 65 (2013), pp. 75--91. (original pdf)
• A. Osękowski, Sharp inequalities for the Haar system and Fourier multipliers, Journal of Function Spaces and Applications 2013 (2013), Article ID 646012, 14 pp. (original pdf)
• A. Osękowski, Sharp inequalities for dyadic A₁ weights, Archiv der Mathematik 101 (2013), pp. 181--190. (original pdf)
• A. Osękowski, A prophet inequality for L²-martingales, Statistics and Probability Letters 83 (2013), pp. 2319--2323. (original pdf)
• A. Osękowski, Sharp inequalities for the dyadic square function in the BMO setting, Acta Mathematica Hungarica 139 (2013), pp. 85--105. (original pdf)
• A. Osękowski, A sharp maximal inequality for continuous martingales and their differential subordinates, Czechoslovak Mathematical Journal 63, no. 4 (2013), pp. 1001-1018. (original pdf)
• A. Osękowski, On martingales whose exponential processes satisfy Muckenhoupt's condition A₁, Statistics and Probability Letters 83 (2013), pp. 1849--1853. (original pdf)
• A. Osękowski, Sharp inequalities for geometric maximal operators associated with general measures, Analysis Mathematica 39 (2013), pp. 287--296. (original pdf)
• A. Osękowski, Logarithmic inequalities for second-order Riesz transforms and related Fourier multipliers, Colloquium Mathematicum 130 (2013), pp. 103--126. (original pdf)
• A. Osękowski, A sharp one-sided bound for the Hilbert transform, Proceedings of the American Mathematical Society 141 (2013), pp. 873--882. (original pdf)
• A. Osękowski, Comparison-type theorems for Itô processes and differentially subordinated semimartingales, ALEA: American Latin Journal of Probability and Mathematical Statistics 10 (2013), pp. 391--414. (original pdf)
• A. Osękowski, Sharp estimates for the functions of bounded lower oscillation, Bulletin of the Australian Mathematical Society 87 (2013), pp. 68--81.
• A. Osękowski, Sharp maximal inequalities for continuous-path semimartingales, Mathematical Inequalities and Applications 16 (2013), pp. 69--92. (original pdf)

2012

• A. Osękowski, Sharp weak type inequalities for Hilbert transform and Riesz projection, Israel Journal of Mathematics 192 (2012), pp. 429--448. (original pdf)
• A. Osękowski, Weak Φ-inequalities for the Haar system and differentially subordinated martingales, Proceedings of the Japan Academy, Series A 88 (2012), pp. 139--144. (original pdf)
• A. Osękowski, Best constants in the weak-type estimates for uncentered maximal operators, Glasgow Mathematical Journal 54 (2012), pp. 655--663. (original pdf)
• A. Osękowski, Sharp inequalities for differentially subordinate harmonic functions and martingales, Canadian Mathematical Bulletin 55 (2012), pp. 597--610. (original pdf)
• A. Osękowski, On the best constants in the weak type inequalities for re-expansion operator and Hilbert transform, Transactions of the American Mathematical Society 364 (2012), pp. 4303--4322. (original pdf)
• A. Osękowski, Sharp logarithmic inequalities for Riesz transforms, Journal of Functional Analysis 263 (2012), pp. 89--108. (original pdf)
• A. Osękowski, Weak type (p,q)-inequalities for the Haar system and differentially subordinated martingales, Mathematische Nachrichten 285 (2012), pp. 794--807. (original pdf)
• A. Osękowski, Doob-type estimates for differentially subordinated martingales, Stochastic Analysis and Applications 30 (2012), pp. 426--447. (original pdf)
• A. Osękowski, A note on Burkholder-Rosenthal inequality, Bulletin of the Polish Academy of Sciences Mathematics 60 (2012), pp. 177--185. (original pdf)
• A. Osękowski, Sharp weak type inequalities for the Haar system and related estimates for non-symmetric martingale transforms, Proceedings of the American Mathematical Society 140 (2012), pp. 2513--2526. (original pdf)
• A. Osękowski, Best constants in the weak type inequalities for a martingale conditional square function, Statistics and Probability Letters 82 (2012), pp. 885--893. (original pdf)
• A. Osękowski, Best constant in Zygmund's inequality and related estimates for orthogonal harmonic functions and martingales, Journal of the Korean Mathematical Society 49 (2012), pp. 659--670. (original pdf)
• A. Osękowski, Logarithmic estimates for the Hilbert transform and the Riesz projection, Archiv der Mathematik 98 (2012), pp. 153--161. (original pdf)
• R. Bañuelos, A. Osękowski, Martingales and sharp bounds for Fourier multipliers, Annales Academiae Scientiarum Fennicae Mathematica 37 (2012), pp. 251--263. (original pdf)
• A. Osękowski, Weak norm inequalities for martingales and geometry of Banach spaces, Statistics and Probability Letters 82 (2012), pp. 411--418. (original pdf).
• A. Osękowski, Inequalities for martingale transforms and related characterizations of Hilbert spaces, Statistics and Probability Letters 82 (2012), pp. 186--190. (original pdf)

2011

• A. Osękowski, A weak-type inequality for orthogonal submartingales and subharmonic functions, Bulletin of the Polish Academy of Sciences Mathematics 59 (2011), pp. 261--274. (original pdf)
• A. Osękowski, A sharp weak-type bound for Ito processes and subharmonic functions, Kyoto Journal of Mathematics 51 (2011), pp. 875--890. (original pdf)
• A. Osękowski, Weak type inequality for the martingale square function and a related characterization of Hilbert spaces, Probability and Mathematical Statistics 31 (2011), pp. 227--238. (original pdf)
• A. Osękowski, Sharp maximal inequalities for the moments of martingales and nonnegative submartingales, Bernoulli Journal of Mathematics 17 (2011), pp. 1327--1343. (original pdf).
• A. Osękowski, On relaxing the assumption of differential subordination in some martingale inequalities, Electronic Communications in Probability 16 (2011), pp. 9--21. (original pdf)
• A. Osękowski, Maximal inequalities for continuous martingales and their differential subordinates, Proceedings of the American Mathematical Society 139 (2011), pp. 721--734. (original pdf)
• A. Osękowski, Sharp and strict L^p-inequalities for Hilbert-space-valued orthogonal martingales, Electronic Journal of Probability 16 (2011), pp. 531--551. (original pdf)
• A. Osękowski, A maximal inequality for nonnegative sub- and supermartingales, Mathematical Inequalities and Applications 14 (2011), pp. 595--604. (original pdf).
• A. Osękowski, Logarithmic estimates for submartingales and their differential subordinates , Journal of Theoretical Probability 24 (2011), pp. 849--874. (original pdf).
• A. Osękowski, Sharp maximal inequality for nonnegative martingales, Statistics and Probability Letters 81 (2011), pp. 1945--1952. (original pdf).

2010

• A. Osękowski, Sharp inequality for martingale maximal functions and stochastic integrals, Illinois Journal of Mathematics, volume in honour of Donald L. Burkholder 54 (2010), pp. 1133--1156. (original pdf).
• A. Osękowski, Maximal inequalities for stochastic integrals, Bulletin of the Polish Academy of Sciences Mathematics 58 (2010), pp. 273--287. (original pdf).
• A. Osękowski, Sharp maximal inequalities for the martingale square bracket, Stochastics: An International Journal of Probability and Stochastic Processes 82 (2010), pp. 589--605. (original pdf)
• A. Osękowski, Sharp moment inequalities for differentially subordinated martingales, Studia Mathematica 201 (2010), pp. 103--131. (original pdf)
• A. Osękowski, Weak type inequalities for conditionally symmetric martingales, Statistics and Probability Letters 80, Vol. 8 (2010), pp. 2009--2013. (original pdf)
• A. Osękowski, Sharp tail inequalities for nonnegative submartingales and their strong differential subordinates, Electronic Communications in Probability 15 (2010), pp. 508--521. (original pdf)
• A. Osękowski, Sharp inequalities for sums of nonnegative random variables and for a martingale conditional square function, ALEA: Latin American Journal of Probability and Mathematical Statistics 7 (2010), pp. 243--256. (original pdf)
• A. Osękowski, Sharp maximal bound for continuous martingales, Statistics and Probability Letters 80, Vol. 4 (2010), pp. 1405--1408. (original pdf)
• A. Osękowski, Sharp ratio inequalities for a conditionally symmetric martingale, Bulletin of the Polish Academy of Sciences Mathematics 58, Vol. 1 (2010), pp. 65--77. (original pdf).
• A. Osękowski, Sharp inequalities for the square function of a nonnegative martingale, Probability and Mathematical Statistics 30, Vol. 1 (2010), pp. 61--72. (original pdf).
• A. Osękowski, Logarithmic estimates for nonsymmetric martingale transforms, Statistics and Probability Letters 80, Vol. 4 (2010), pp. 678--682. (original pdf)

2009

• A. Osękowski, Strong differential subordination and sharp inequalities for orthogonal processes , Journal of Theoretical Probability 22, Vol. 4 (2009), pp. 837--855. (original pdf)
• A. Osękowski, Sharp weak type inequalities for differentially subordinated martingales, Bernoulli Journal of Mathematics 15, Vol. 3 (2009), pp. 871--897. (original pdf)
• A. Osękowski, Sharp norm comparison of the maxima of a sequence and its predictable projection, Statistics and Probability Letters 79 Vol. 16 (2009), pp. 1784--1788. (original pdf)
• A. Osękowski, Weak type inequality for the square function of a nonnegative submartingale , Bulletin of the Polish Academy of Sciences Mathematics 57, Vol. 1 (2009), pp. 81--89. (original pdf)
• A. Osękowski, On the best constant in the weak type inequality for the square function of a conditionally symmetric martingale, Statistics and Probability Letters 79 (2009), pp. 1536--1538. (original pdf)
• A. Osękowski, Sharp norm inequalities for Stochastic integrals in which the integrator is a nonnegative supermartingale, Probability and Mathematical Statistics 29, Vol. 1 (2009), pp. 29--42. (original pdf)
• A. Osękowski, Sharp Maximal Inequality for Martingales and Stochastic Integrals, Electronic Communications in Probability 14 (2009), pp. 17--30. (original pdf)

2008

• A. Osękowski, Sharp LlogL inequality for Differentially Subordinated Martingales, Illinois Journal of Mathematics 52, Vol. 3 (2008), pp. 745--756. (original pdf)
• A. Osękowski, Sharp inequality for bounded submartingales and their differential subordinates, Electronic Communications in Probability 13 (2008), pp. 660--675. (original pdf)
• A. Osękowski, Sharp norm inequality for bounded submartingales, Journal of Inequalities in Pure and Applied Mathematics (JIPAM) 9 Vol. 4 (2008), art. 93. (original pdf)
• A. Osękowski, On Φ-inequalities for Bounded Submartingales and Subharmonic Functions, Communications of the Korean Mathematical Society 23, Vol. 2 (2008) , pp. 269--277. (original pdf)
• A. Osękowski, Weak type inequality for noncommutative differentially subordinated martingales, Probability Theory and Related Fields 140 (2008), pp. 553 -- 568. (original pdf)
• A. Osękowski, Sharp maximal inequality for stochastic integrals, Proceedings of the American Mathematical Society 136 (2008), pp. 2951--2958. (original pdf)

2007

• A. Osękowski, Sharp Norm Inequalities for Martingales and their Differential Subordinates, Bulletin of the Polish Academy of Sciences Mathematics 55 (2007), pp. 373--385. (original pdf)
• A. Osękowski, Inequalities for dominated martingales, Bernoulli Journal of Mathematics 13, Vol. 1 (2007), pp. 54--79. (original pdf)

2005

• A. Osękowski, Two inequalities for the first moment of a martingale, its square and maximal function, Bulletin of the Polish Academy of Sciences Mathematics 53 (2005), pp. 441--449. (original pdf)

Publications to appear

• R. Bañuelos, A. Osękowski, Weighted square function estimates, to appear in Bulletin des Sciences Mathématiques.