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

Bingyang Hu; Zhenghui Huo; Loredana Lanzani; Kevin Palencia; Nathan A. Wagner

doi:10.1016/j.jfa.2023.110177

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

Bingyang Hu, Zhenghui Huo, Loredana Lanzani, Kevin Palencia, Nathan A. Wagner

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Consider a bounded, strongly pseudoconvex domain D⊂Cⁿ with minimal smoothness (namely, the class C²) 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.

Original language	English (US)
Article number	110177
Journal	Journal of Functional Analysis
Volume	286
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2023.110177
State	Published - Jan 1 2024

Keywords

Bergman projection
Commutator
Hankel
Strongly pseudoconvex

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2023.110177

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title = "The commutator of the Bergman projection on strongly pseudoconvex domains with minimal smoothness",

abstract = "Consider a bounded, strongly pseudoconvex domain D⊂Cn with minimal smoothness (namely, the class C2) and let b be a locally integrable function on D. We characterize boundedness (resp., compactness) in Lp(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.",

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T1 - The commutator of the Bergman projection on strongly pseudoconvex domains with minimal smoothness

AU - Hu, Bingyang

AU - Huo, Zhenghui

AU - Lanzani, Loredana

AU - Palencia, Kevin

AU - Wagner, Nathan A.

PY - 2024/1/1

Y1 - 2024/1/1

N2 - Consider a bounded, strongly pseudoconvex domain D⊂Cn with minimal smoothness (namely, the class C2) and let b be a locally integrable function on D. We characterize boundedness (resp., compactness) in Lp(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.

AB - Consider a bounded, strongly pseudoconvex domain D⊂Cn with minimal smoothness (namely, the class C2) and let b be a locally integrable function on D. We characterize boundedness (resp., compactness) in Lp(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.

KW - Bergman projection

KW - Commutator

KW - Hankel

KW - Strongly pseudoconvex

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

Abstract

Keywords

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