L𝑝-extrapolation of non-local operators : maximal regularity of elliptic integrodifferential operators with measurable coefficients
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Abstract
The aim of this article is to deepen the understanding of the derivation of Lp-estimates of non-local operators. We review the Lp-extrapolation theorem of Shen (2005) which builds on a real variable argument of Caffarelli and Peral (1998) 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 (2015). As an application, we prove resolvent estimates and maximal regularity properties in Lp-spaces of non-local elliptic integrodifferential operators.
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Journal of evolution equations, 21, Springer, Basel, 2021, https://doi.org/10.1007/s00028-020-00609-7