Abstract
Singular integral operators with piecewise continuous matrix coefficients are considered on a piecewise smooth curve in weighted Lebesgue spaces. In contrast to the classical case, the operators have generalized Cauchy kernels arising as a parametrix of first-order elliptic systems in the plane. A Fredholmness criterion and an index formula for these operators are obtained in weighted Lebesgue spaces.
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Translated by I. Ruzanova
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Soldatov, A.P. Singular Integral Operators with a Generalized Cauchy Kernel. Dokl. Math. 105, 117–122 (2022). https://doi.org/10.1134/S1064562422020168
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DOI: https://doi.org/10.1134/S1064562422020168