Weighted Lp estimates for the Bergman and Szegő projections on strongly pseudoconvex domains with near minimal smoothness

Abstract

We prove the weighted Lp regularity of the ordinary Bergman and Cauchy-Szegő projections on strongly pseudoconvex domains D in Cn with near minimal smoothness for appropriate generalizations of the Bp/Ap classes. In particular, the Bp/Ap Muckenhoupt type condition is expressed relative to balls in a quasi-metric that arises as a space of homogeneous type on either the interior or the boundary of the domain D.