Hölder estimates for the ¯ ∂-equation with a support condition

A Holder estimate for solutions to au — a in weakly pseudo-convex domains is obtained when the restriction of a to the boundary vanishes near the set of degeneracy of the Levi form. Applications are given to holomorphic approximation and divi-sion problems. l Introduction * Holder estimates for the equation du = a in a strictly pseudoconvex domain D were first obtained by Kerzman [8] and Lieb [11], and were later sharpened by Romanov and Henkin [16]. In the weakly pseudoconvex case, analogous results were obtained by Range [15] by assuming that the support of is