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

2016/09/27 by Rodrigo Bañuelos, Banuelos, Rodrigo, Adam Osękowski +1
Mathematics · Computer Science · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1609.08672

Abstract

We study stability estimates for the almost extremal functions associated\nwith the L^p-bound for the real and imaginary parts of the Beurling-Ahlfors\noperator. The proof exploits probabilistic methods and rests on analogous\nresults for differentially subordinate martingales which are of independent\ninterest. This allows us to obtain stability inequalities for a larger class of\nFourier multipliers.\n

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