Ψ-weighted Cauchy-Riemann operators and some associated integral representation. Issue 3 (3rd March 2020) - Ariza, Eusebio; Di Teodoro, Antonio; Vanegas, Carmen Judith
Abstract: 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.