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

被引：4

作者：

Douglas, Ronald G. ^{[1
]}

Guo, Kunyu ^{[2
]}

Wang, Yi ^{[3
]}

机构：

[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[3] Chongqing Univ, Dept Math, Chongqing 400044, Peoples R China

来源：

ADVANCES IN MATHEMATICS | 2022年 / 407卷

基金：

美国国家科学基金会; 中国国家自然科学基金;

关键词：

Arveson-Douglas conjecture; Complex harmonic analysis; Bergman spaces; Strongly pseudoconvex domains; HANKEL-OPERATORS;

D O I：

10.1016/j.aim.2022.108546

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：41

共 30 条

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[29] Estimates of the Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{L^p}$$\end{document} Norms of the Bergman Projection on Strongly Pseudoconvex Domains
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