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

We prove the weighted L-p regularity of the ordinary Bergman and Cauchy-Szego projections on strongly pseudoconvex domains D in 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. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This paper proves the weighted L-p regularity of the ordinary Bergman and Cauchy-Szego projections on strongly pseudoconvex domains D in C-n with near minimal smoothness for appropriate generalizations of the B-p/A(p) classes. Specifically, 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.