Abstract
In this article, we first give a modified Schwarz–Pompeiu formula in a general sector ring with angle \(\vartheta =\frac{\pi }{\alpha },\ \alpha \ge 1/2\) by proper conformal mappings, and obtain the solution of the Schwarz problem for the Cauchy–Riemann equation in explicit forms. Furthermore, we construct some integral operators and discuss their properties in detail. Finally, by virtue of these operators, Schwarz problems for an inhomogeneous polyanalytic equation and for a generalized polyanalytic equation are investigated, respectively.
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