L^p-extrapolation of non-local operators: Maximal regularity of elliptic integrodifferential operators with measurable coefficients

2020/04/23 by Patrick Tolksdorf, Tolksdorf, Patrick
Mathematics · #Advanced Harmonic Analysis Research #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.AP #math.CA #math.FA

paper · pdf · doi:10.48550/arxiv.2004.11174

17 pages

arxiv created 2020/04/23 · arxiv updated 2020/04/24

Abstract

The aim of this article is to deepen the understanding of the derivation of L^p-estimates of non-local operators. We review the L^p-extrapolation theorem of Shen which builds on a real variable argument of Caffarelli and Peral and adapt this theorem to account for non-local weak reverse Hölder estimates. These non-local weak reverse Hölder estimates appear for example in the investigation of non-local elliptic integrodifferential operators. This originates from the fact that here only a non-local Caccioppoli inequality is valid, see Kuusi, Mingione, and Sire. As an application, we prove resolvent estimates and maximal regularity properties in L^p-spaces of non-local elliptic integrodifferential operators.

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