ψ-weighted Cauchy-Riemann operators and some associated integral representation

Eusebio Ariza, Antonio Di Teodoro, Carmen Judith Vanegas

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Resumen

In the present work we introduce a weighted Cauchy-Riemann type operator in the complex plane, where the weights are complex non-constant functions. We construct a fundamental solution for this operator where the weights are complex constant functions and orthogonal functions inspired by the idea for the construction of the Levy function proposed by Miranda (see [23]). Therefore we obtain a Cauchy-Pompeiu integral representation formula. We also present some examples of such representations when we take some particular weights.

Idioma originalInglés
Páginas (desde-hasta)335-360
Número de páginas26
PublicaciónQuaestiones Mathematicae
Volumen43
N.º3
DOI
EstadoPublicada - 3 mar. 2020

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