Hölder estimates for homotopy operators on strictly pseudoconvex domains with $C^2$ boundary

Abstract

We derive a new homotopy formula for a strictly pseudoconvex domain of C 2 boundary in C n by using a method of Lieb and Range and obtain estimates in Lipschitz spaces for the homotopy operators. For r > 1 and q > 0, we obtain a Λ r+1/2 solution u to ∂u = f for a ∂-closed (0, q)-form f of class Λ r in the domain. We apply the estimates to obtain boundary regularities of D-solutions for a domain in C n × R m .