Weighted $L^p$ Estimates for the Bergman and Szegő Projections on Strongly Pseudoconvex Domains with Near Minimal Smoothness

Abstract

We prove the weighted $L^p$ regularity of the ordinary Bergman and Cauchy-Szegő projections on strongly pseudoconvex domains $D$ in ${\mathbb{C}}^n$ with near minimal smoothness for appropriate generalizations of the $B_p/A_p$ classes. In particular, the $B_p/A_p$ 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 $D$.

arXiv comment40 pages, introduction reorganized and some typos corrected