English

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 Φ\Phi-inequalities in the spirit of Bourgain and Brezis, we establish some Φ\Phi-inequalities for fractional martingale transforms. These inequalities may be thought of as martingale models of Φ\Phi-inequalities for differential operators. The proofs rest on new simple Bellman functions.

Keywords

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