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).
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Translated by E. Oborin
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Petrosyan, A.I. On the Derivatives of Cauchy-Type Integrals in the Polydisk. J. Contemp. Mathemat. Anal. 55, 303–306 (2020). https://doi.org/10.3103/S1068362320050040
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DOI: https://doi.org/10.3103/S1068362320050040