Estimates of the harmonic Bergman kernel on smooth domains

Hyeonbae Kang; Hyungwoon Koo

doi:10.1006/jfan.2001.3761

Estimates of the harmonic Bergman kernel on smooth domains

Hyeonbae Kang, Hyungwoon Koo

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

33 Citations (Scopus)

Abstract

We obtain optimal size estimates of the harmonic Bergman kernel and its derivatives on smooth domains. Based on these estimates we derive mapping properties of the harmonic Bergman projection on Lebesgue spaces and Lipschitz spaces.

Original language	English
Pages (from-to)	220-239
Number of pages	20
Journal	Journal of Functional Analysis
Volume	185
Issue number	1
DOIs	https://doi.org/10.1006/jfan.2001.3761
Publication status	Published - 2001 Sept 10

Bibliographical note

Funding Information:
1The first author’s research was partially supported by KOSEF 98-0701-03-01-5 and a grant from SNU and the second author’s research was partially supported by KOSEF 981-0102-009-2. We thank the referee for pointing out the relevance of Lemma 3.1 in [FR] to Theorem 4.2 of this paper. We also thank Professor D. Sarason for helpful suggestions.

Keywords

Biharmonic equations
Harmonic Bergman kernel
Harmonic Bergman projection

ASJC Scopus subject areas

Analysis

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10.1006/jfan.2001.3761

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abstract = "We obtain optimal size estimates of the harmonic Bergman kernel and its derivatives on smooth domains. Based on these estimates we derive mapping properties of the harmonic Bergman projection on Lebesgue spaces and Lipschitz spaces.",

keywords = "Biharmonic equations, Harmonic Bergman kernel, Harmonic Bergman projection",

author = "Hyeonbae Kang and Hyungwoon Koo",

note = "Funding Information: 1The first author{\textquoteright}s research was partially supported by KOSEF 98-0701-03-01-5 and a grant from SNU and the second author{\textquoteright}s research was partially supported by KOSEF 981-0102-009-2. We thank the referee for pointing out the relevance of Lemma 3.1 in [FR] to Theorem 4.2 of this paper. We also thank Professor D. Sarason for helpful suggestions.",

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AB - We obtain optimal size estimates of the harmonic Bergman kernel and its derivatives on smooth domains. Based on these estimates we derive mapping properties of the harmonic Bergman projection on Lebesgue spaces and Lipschitz spaces.

KW - Biharmonic equations

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Estimates of the harmonic Bergman kernel on smooth domains

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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