The commutator of the Bergman projection on strongly pseudoconvex domains with minimal smoothness

被引：1

作者：

Hu, Bingyang ^{[1
]}

Huo, Zhenghui ^{[2
]}

Lanzani, Loredana ^{[3
,4
]}

Palencia, Kevin ^{[5
]}

Wagner, Nathan A. ^{[6
]}

机构：

[1] Purdue Univ, Dept Math, 150 Univ Ave, W Lafayette, IN 47907 USA

[2] Duke Kunshan Univ, Zu Chongzhi Ctr Math & Comp Sci, Div Nat & Appl Sci, 8 Duke Ave, Kunshan, Jiangsu, Peoples R China

[3] Syracuse Univ, Dept Math, Syracuse, NY USA

[4] Univ Bologna, Dipartimento Matemat, Bologna, Italy

[5] Northern Illinois Univ, Dept Math Sci, 1425 W Lincoln Hwy, De Kalb, IL 60115 USA

[6] Brown Univ, Dept Math, 151 Thayer St, Providence, RI 02912 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2024年 / 286卷 / 01期

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

Bergman projection; Commutator; Hankel; Strongly pseudoconvex; HANKEL-OPERATORS; SZEGO PROJECTIONS; BOUNDARY-BEHAVIOR; L-P; KERNEL; BMO; SPACES;

D O I：

10.1016/j.jfa.2023.110177

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider a bounded, strongly pseudoconvex domain D subset of C-n with minimal smoothness (namely, the class C-2) and let b be a locally integrable function on D. We characterize boundedness (resp., compactness) in L-p(D), p>1, of the commutator [b,P] of the Bergman projection P in terms of an appropriate bounded (resp. vanishing) mean oscillation requirement on b. We also establish the equivalence of such notion of BMO (resp., VMO) with other BMO and VMO spaces given in the literature. Our proofs use a dyadic analog of the Berezin transform and holomorphic integral representations going back (for smooth domains) to N. Kerzman & E. M. Stein, and E. Ligocka.(c) 2023 Elsevier Inc. All rights reserved.

引用

页数：45

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