On the p-essential normality of principal submodules of the Bergman module on strongly pseudoconvex domains

In this paper, we show that under a mild condition, a principal submodule of the Bergman module on a bounded strongly pseudoconvex domain with smooth boundary in C-n is p -essentially normal for all p > n. This improves a previous result by the first author and K. Wang, in which it was shown that any polynomial-generated principal submodule of the Bergman module on the unit ball B-n is p -essentially normal for all p > n. As a consequence, we show that the submodule of L-a(2)(B-n) consisting of functions vanishing on an analytic subset of pure codimension 1 is p -essentially normal for all p > n. (C) 2022 Elsevier Inc. All rights reserved.