We consider a class of fully nonlinear integro-differential operators where the nonlocal integral has two components: the non-degenerate one corresponds to the $\alpha$-stable operator and the second one (possibly degenerate) corresponds to a class of lower order Lévy measures. Such operators do not have a global scaling property. We establish Hölder regularity, Harnack inequality and boundary Harnack property of solutions of these operators.

中文翻译：

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非线性摄动稳定型算子的正则结果

我们考虑一类完全非线性的积分微分算子，其中非局部积分具有两个成分：非简并一个对应于$ \ alpha $ -stable运算符，第二个（可能简并）对应于一类低阶Lévy措施。此类运算符不具有全局缩放属性。我们建立了这些算子解的Hölder正则性，Harnack不等式和边界Harnack性质。