On $\Phi$-inequalities for martingale fractional integration and their Bellman functions
Classical Analysis and ODEs
2021-07-21 v1 Probability
Abstract
Inspired by a conjecture of Vladimir Maz'ya on -inequalities in the spirit of Bourgain and Brezis, we establish some -inequalities for fractional martingale transforms. These inequalities may be thought of as martingale models of -inequalities for differential operators. The proofs rest on new simple Bellman functions.
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Cite
@article{arxiv.2107.09336,
title = {On $\Phi$-inequalities for martingale fractional integration and their Bellman functions},
author = {Dmitriy Stolyarov},
journal= {arXiv preprint arXiv:2107.09336},
year = {2021}
}
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16 pages