Equivalence of extremal problems on BMO and estimates of martingale transform of bounded martingales

Speaker(s)

Vasily Vasyunin

Affiliation

St. Petersburg State University

Date

April 11, 2019, 12:15 p.m.

Room

room 3260

Seminar

Seminar of Probability Group

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The purpose of the talk is to study the interplay between
the following two extremal problems, arising in the context of analysis
and probability:

1) Find the supremum of an f-functional over the class of all BMO
functions with prescribed averages.

2) Find the supremum of an f-functional over the class of martingale
transforms of bounded martingales, with prescribed averages.

These two absolutely different problems appear to be equivalent: for any
given functional f, the solution each of them can be easily rewritten into
the solution of the other one.

This is a joint result with D. Stolyarov and P. Zatitskii.

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