The weighted Bergman kernels and projections on a class of unbounded Hartogs domains

Abstract

In this paper, we study the weighted Bergman kernels and projections on a class of unbounded Hartogs domains. As applications of our main results, we can obtain the explicit formulas for the weighted Bergman kernels on a wide class of unbounded Hartogs domains with different types of weight functions, and show that the associated weighted Bergman projections are bounded on the weighted [Formula: see text] spaces if and only if [Formula: see text].