The explicit solutions of$C_{p,q}^{k + \alpha }$-form for the$\bar \partial$-equations on pseudoconvex open sets

Abstract

In this paper, we study the integral solution operators for the$\bar \partial$-equations on pseudoconvex domains. As a generalization of [1] for the$\bar \partial$-equations on pseudoconvex domains with boundary of classC ^∞, we obtain the explicit integral operator solutions of$C_{p,q}^{k + \alpha }$-form for the$\bar \partial$-equations on pseudoconvex open sets with boundary ofC ^k (k≥0) and the sup-norm estimates of which solutions have similar as that [1] in form.