论文标题
$ \ mathrm {l}^p $ - 非本地运算符的分解：具有可测量系数
$\mathrm{L}^p$-extrapolation of non-local operators: Maximal regularity of elliptic integrodifferential operators with measurable coefficients
论文作者
论文摘要
本文的目的是加深对非本地运算符的$ \ mathrm {l}^p $估计的推导的理解。我们回顾了$ \ mathrm {l}^p $ - 口气定理，该定理基于caffarelli和peral的真实变量参数，并适应了该定理以说明非本地弱反向hölder估计。这些非本地弱反向Hölder估计值例如在研究非本地椭圆综合差异算子中。这源于以下事实：这里只有非本地caccioppoli不平等现象是有效的，请参见Kuusi，Mingione和Sire。作为一个应用程序，我们证明了$ \ mathrm {l}^p $ - 非本地椭圆综合差异操作员的分解估计和最大规则性属性。
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 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 $\mathrm{L}^p$-spaces of non-local elliptic integrodifferential operators.
