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arXiv · 1609.08672

Stability in Burkholder's differentially subordinate martingales inequalities and applications to Fourier multipliers

Rodrigo Banuelos·Adam Osekowski
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Abstract

We study stability estimates for the almost extremal functions associated with the $L^p$-bound for the real and imaginary parts of the Beurling-Ahlfors operator. The proof exploits probabilistic methods and rests on analogous results for differentially subordinate martingales which are of independent interest. This allows us to obtain stability inequalities for a larger class of Fourier multipliers.

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Rodrigo Banuelos, Adam Osekowski. 2016-09-27. Stability in Burkholder's differentially subordinate martingales inequalities and applications to Fourier multipliers. https://arxiv.org/abs/1609.08672

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