Weighted estimates of the Bergman projection with matrix weights

Zhenghui Huo; Brett D. Wick

doi:10.1090/conm/799/16020

Weighted estimates of the Bergman projection with matrix weights

Zhenghui Huo, Brett D. Wick

Department of Mathematics & Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

We establish a weighted inequality for the Bergman projection with matrix weights for a class of pseudoconvex domains. We extend a result of Aleman and Constantin and obtain the following estimate for the weighted norm of P: ∥P∥L₂(Ω,W)≤C(B2(W))². Here B₂(W) is the Bekollé–Bonami constant for the matrix weight W and C is a constant that is independent of the weight W but depends upon the dimension and the domain.

Original language	English
Title of host publication	Recent Progress in Function Theory and Operator Theory - AMS Special Session Recent Progress in Function Theory and Operator Theory, 2022
Editors	Alberto A. Condori, Elodie Pozzi, William T. Ross, Alan A. Sola
Publisher	American Mathematical Society
Pages	53-73
Number of pages	21
ISBN (Print)	9781470472467
DOIs	https://doi.org/10.1090/conm/799/16020
State	Published - 2024
Event	AMS Special Session on Recent Progress in Function Theory and Operator Theory, 2022 - Virtual, Online Duration: Apr 6 2022 → Apr 6 2022

Publication series

Name	Contemporary Mathematics
Volume	799
ISSN (Print)	0271-4132
ISSN (Electronic)	1098-3627

Conference

Conference	AMS Special Session on Recent Progress in Function Theory and Operator Theory, 2022
City	Virtual, Online
Period	04/6/22 → 04/6/22

Keywords

Bergman kernel
Bergman projection
weighted inequality

Access to Document

10.1090/conm/799/16020

Cite this

Huo, Z., & Wick, B. D. (2024). Weighted estimates of the Bergman projection with matrix weights. In A. A. Condori, E. Pozzi, W. T. Ross, & A. A. Sola (Eds.), Recent Progress in Function Theory and Operator Theory - AMS Special Session Recent Progress in Function Theory and Operator Theory, 2022 (pp. 53-73). (Contemporary Mathematics; Vol. 799). American Mathematical Society. https://doi.org/10.1090/conm/799/16020

Huo, Zhenghui ; Wick, Brett D. / Weighted estimates of the Bergman projection with matrix weights. Recent Progress in Function Theory and Operator Theory - AMS Special Session Recent Progress in Function Theory and Operator Theory, 2022. editor / Alberto A. Condori ; Elodie Pozzi ; William T. Ross ; Alan A. Sola. American Mathematical Society, 2024. pp. 53-73 (Contemporary Mathematics).

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title = "Weighted estimates of the Bergman projection with matrix weights",

abstract = "We establish a weighted inequality for the Bergman projection with matrix weights for a class of pseudoconvex domains. We extend a result of Aleman and Constantin and obtain the following estimate for the weighted norm of P: ∥P∥L2(Ω,W)≤C(B2(W))2. Here B2(W) is the Bekoll{\'e}–Bonami constant for the matrix weight W and C is a constant that is independent of the weight W but depends upon the dimension and the domain.",

keywords = "Bergman kernel, Bergman projection, weighted inequality",

author = "Zhenghui Huo and Wick, {Brett D.}",

note = "Publisher Copyright: {\textcopyright} 2024 American Mathematical Society.; AMS Special Session on Recent Progress in Function Theory and Operator Theory, 2022 ; Conference date: 06-04-2022 Through 06-04-2022",

year = "2024",

doi = "10.1090/conm/799/16020",

language = "English",

isbn = "9781470472467",

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editor = "Condori, {Alberto A.} and Elodie Pozzi and Ross, {William T.} and Sola, {Alan A.}",

booktitle = "Recent Progress in Function Theory and Operator Theory - AMS Special Session Recent Progress in Function Theory and Operator Theory, 2022",

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Huo, Z & Wick, BD 2024, Weighted estimates of the Bergman projection with matrix weights. in AA Condori, E Pozzi, WT Ross & AA Sola (eds), Recent Progress in Function Theory and Operator Theory - AMS Special Session Recent Progress in Function Theory and Operator Theory, 2022. Contemporary Mathematics, vol. 799, American Mathematical Society, pp. 53-73, AMS Special Session on Recent Progress in Function Theory and Operator Theory, 2022, Virtual, Online, 04/6/22. https://doi.org/10.1090/conm/799/16020

Weighted estimates of the Bergman projection with matrix weights. / Huo, Zhenghui; Wick, Brett D.
Recent Progress in Function Theory and Operator Theory - AMS Special Session Recent Progress in Function Theory and Operator Theory, 2022. ed. / Alberto A. Condori; Elodie Pozzi; William T. Ross; Alan A. Sola. American Mathematical Society, 2024. p. 53-73 (Contemporary Mathematics; Vol. 799).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Wick, Brett D.

PY - 2024

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N2 - We establish a weighted inequality for the Bergman projection with matrix weights for a class of pseudoconvex domains. We extend a result of Aleman and Constantin and obtain the following estimate for the weighted norm of P: ∥P∥L2(Ω,W)≤C(B2(W))2. Here B2(W) is the Bekollé–Bonami constant for the matrix weight W and C is a constant that is independent of the weight W but depends upon the dimension and the domain.

AB - We establish a weighted inequality for the Bergman projection with matrix weights for a class of pseudoconvex domains. We extend a result of Aleman and Constantin and obtain the following estimate for the weighted norm of P: ∥P∥L2(Ω,W)≤C(B2(W))2. Here B2(W) is the Bekollé–Bonami constant for the matrix weight W and C is a constant that is independent of the weight W but depends upon the dimension and the domain.

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KW - Bergman projection

KW - weighted inequality

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DO - 10.1090/conm/799/16020

M3 - Conference contribution

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SN - 9781470472467

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SP - 53

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BT - Recent Progress in Function Theory and Operator Theory - AMS Special Session Recent Progress in Function Theory and Operator Theory, 2022

A2 - Condori, Alberto A.

A2 - Pozzi, Elodie

A2 - Ross, William T.

A2 - Sola, Alan A.

PB - American Mathematical Society

T2 - AMS Special Session on Recent Progress in Function Theory and Operator Theory, 2022

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Huo Z, Wick BD. Weighted estimates of the Bergman projection with matrix weights. In Condori AA, Pozzi E, Ross WT, Sola AA, editors, Recent Progress in Function Theory and Operator Theory - AMS Special Session Recent Progress in Function Theory and Operator Theory, 2022. American Mathematical Society. 2024. p. 53-73. (Contemporary Mathematics). doi: 10.1090/conm/799/16020

Weighted estimates of the Bergman projection with matrix weights

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