$\mathrm{L}^p$-extrapolation of non-local operators: Maximal regularity of elliptic integrodifferential operators with measurable coefficients

Patrick Tolksdorf

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arXiv · 2004.11174

$\mathrm{L}^p$-extrapolation of non-local operators: Maximal regularity of elliptic integrodifferential operators with measurable coefficients

Patrick Tolksdorf

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Abstract

The aim of this article is to deepen the understanding of the derivation of $\mathrm{L}^p$-estimates of non-local operators. We review the $\mathrm{L}^p$-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 H\"older estimates. These non-local weak reverse H\"older 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 $\mathrm{L}^p$-spaces of non-local elliptic integrodifferential operators.

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Patrick Tolksdorf. 2020-04-23. $\mathrm{L}^p$-extrapolation of non-local operators: Maximal regularity of elliptic integrodifferential operators with measurable coefficients. https://arxiv.org/abs/2004.11174

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