12 citations · 41 across the 31 of their papers we have counts for
41 papers
Martingale transforms of bounded random variables and indicator functions of events
Dmitriy Stolyarov, Vasily Vasyunin, Pavel Zatitskii
We provide sharp estimates for the distribution function of a martingale transform of the indicator function of an event. They are formulated in terms of Burkholder functions, whic…
Alberti's type rank one theorem for martingales
Rami Ayoush, Dmitriy Stolyarov, Michał Wojciechowski
We prove that the polar decomposition of the singular part of a vector measure depends on its conditional expectations computed with respect to the -regular filtration. This dep…
Bellman functions on simple non-convex domains in the plane
Paata Ivanisvili, Dmitriy Stolyarov, Vasily Vasyunin +1
The present paper provides a generalization of the previous authors' work on Bellman functions for integral functionals on . Those Bellman functions are the minimal l…
On embedding of Besov spaces of zero smoothness into Lorentz spaces
Dmitriy Stolyarov
We show that the zero smoothness Besov space does not embed into the Lorentz space unless ; here . This answers negatively a quest…
Trace inequalities for Sobolev martingales
Dmitriy Stolyarov
We study limiting trace inequalities in the style of Maz'ya and Meyers--Ziemer for Sobolev martingales. We develop the Bellman function approach to such estimates, which allows to…
On locally concave functions on simplest non-convex domains
Dmitriy Stolyarov, Pavel Zatitskiy
We prove that certain Bellman functions of several variables are the minimal locally concave functions. This generalizes earlier results about Bellman functions of two variables.