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math.PR2022
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…
math.PR2020
Fractional integration for irregular martingales
Dmitriy Stolyarov, Dmitry Yarcev
We suggest two versions of the Hardy--Littlewood--Sobolev inequality for discrete time martingales. In one version, the fractional integration operator is a martingale transform, h…