Vekua integral operators on Riemann surfaces (Q5951066)

In the present paper, the nonhomogeneous Cauchy-Riemann equation \(\overline\partial f=F\) on a Riemann surface in a class of square integrable linear differentials is considered. The author, by using the integral operators which are analogous with the operators introduced by Vekua in his theory of generalized analytic functions gives conditions for the solvability of the equation and a structural formula for the solutions.