Abstract

In the paper the formulas are provided for the derivatives of Cauchy-type integral \(K[u]\) which are smooth on the skeleton of the polydisk of functions \(u\). These formulas express the derivatives of the order \(m\) of \(K[u]\) through the derivatives of lower order (Theorem 2.1). They are used for estimating the smoothness of the derivatives of the Cauchy-type integral in terms of Hölder order scale (Theorem 3.1).

中文翻译：

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关于多圆盘上柯西型积分的导数

摘要

在本文中，提供了柯西型积分\（K [u] \）的导数的公式，这些导数在函数\（u \）的多重圆盘的骨架上是光滑的。这些公式表示顺序的衍生物\（M \）的\（K [U] \）通过低阶的衍生物（定理2.1）。它们用于根据Hölder阶标度（定理3.1）来估计Cauchy型积分的导数的光滑度。