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 (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 \(\mathrm {L}^p\)-spaces of non-local elliptic integrodifferential operators.

本文的目的是加深对非本地运算符\（\ mathrm {L} ^ p \）的推导的理解。我们回顾了Shen（2005）的\（\ mathrm {L} ^ p \）-外推定理，该定理基于Caffarelli和Peral（1998）的实变量论证，并且对该定理进行了调整，以解决非局部弱逆Hölder估计。 。这些非局部弱反向Hölder估计出现在例如非局部椭圆积分微分算子的研究中。这源于以下事实：在这里只有非本地的Caccioppoli不等式有效，请参见Kuusi，Mingione和Sire（2015）。作为应用程序，我们证明了\（\ mathrm {L} ^ p \）中的可分辨估计和最大正则性非局部椭圆积分微分算子的-空间。