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arXiv · 2107.09336

On $\Phi$-inequalities for martingale fractional integration and their Bellman functions

Dmitriy Stolyarov
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Abstract

Inspired by a conjecture of Vladimir Maz'ya on $\Phi$-inequalities in the spirit of Bourgain and Brezis, we establish some $\Phi$-inequalities for fractional martingale transforms. These inequalities may be thought of as martingale models of $\Phi$-inequalities for differential operators. The proofs rest on new simple Bellman functions.

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Dmitriy Stolyarov. 2021-07-20. On $\Phi$-inequalities for martingale fractional integration and their Bellman functions. https://arxiv.org/abs/2107.09336

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