The Vekua– Pompeiu generalized operator

Author(s):  O.V. Chernova, Belgorod State University, Belgorod, Russia,

Issue:  Volume 50, №1

Rubric:  Mathematics

Annotation:  In the article we consider the generalized integral of the Vekua-Pompeiu integral for vector functions from Hölder continuously differentiable class with a weight. It is proved that this integral under certain conditions on a density is continuously differentiable, and it is a solution of the generalized Cauchy-Riemann system. A theorem is declared that for some restrictions on a Hölder power the corresponding integral operator is bounded in Hölder spaces with a certain weight, it is invertible and its inverse is generalized operator Cauchy-Riemann system

Keywords:  The Vekua-Pompeiu generalized integral, weighted Hölder space, the Cauchy-Riemann system, compact embedding

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