Double integral characterizations of harmonic Bergman spaces

Boo Rim Choe; Kyesook Nam

doi:10.1016/j.jmaa.2011.02.024

Double integral characterizations of harmonic Bergman spaces

Boo Rim Choe, Kyesook Nam

Department of Mathematics

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

10 Citations (Scopus)

Abstract

Recently Li et al. have characterized, except for a critical case, the weighted Bergman spaces over the complex ball by means of integrability conditions of double integrals associated with difference quotients of holomorphic functions. In this paper we extend those characterizations to the case of weighted harmonic Bergman spaces over the real ball and complement their results by providing a characterization for the missing critical case. We also investigate the possibility of extensions to the half-space setting. Our observations reveal an interesting half-space phenomenon caused by the unboundedness of the half-space.

Original language	English
Pages (from-to)	889-909
Number of pages	21
Journal	Journal of Mathematical Analysis and Applications
Volume	379
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2011.02.024
Publication status	Published - 2011 Jul 15

Bibliographical note

Funding Information:
✩ The first-named author was supported by Mid-career Researcher Program through NRF grant funded by the MEST (R01-2008-000-20206-0). The second-named author was supported by Basic Science Research Program through NRF grant funded by the MEST (2010-0006518). * Corresponding author. E-mail addresses: cbr@korea.ac.kr (B.R. Choe), ksnam@snu.ac.kr (K. Nam).

Keywords

Unit ball
Upper half-space
Weighted harmonic bergman spaces

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2011.02.024

Cite this

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title = "Double integral characterizations of harmonic Bergman spaces",

abstract = "Recently Li et al. have characterized, except for a critical case, the weighted Bergman spaces over the complex ball by means of integrability conditions of double integrals associated with difference quotients of holomorphic functions. In this paper we extend those characterizations to the case of weighted harmonic Bergman spaces over the real ball and complement their results by providing a characterization for the missing critical case. We also investigate the possibility of extensions to the half-space setting. Our observations reveal an interesting half-space phenomenon caused by the unboundedness of the half-space.",

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author = "Choe, {Boo Rim} and Kyesook Nam",

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N2 - Recently Li et al. have characterized, except for a critical case, the weighted Bergman spaces over the complex ball by means of integrability conditions of double integrals associated with difference quotients of holomorphic functions. In this paper we extend those characterizations to the case of weighted harmonic Bergman spaces over the real ball and complement their results by providing a characterization for the missing critical case. We also investigate the possibility of extensions to the half-space setting. Our observations reveal an interesting half-space phenomenon caused by the unboundedness of the half-space.

AB - Recently Li et al. have characterized, except for a critical case, the weighted Bergman spaces over the complex ball by means of integrability conditions of double integrals associated with difference quotients of holomorphic functions. In this paper we extend those characterizations to the case of weighted harmonic Bergman spaces over the real ball and complement their results by providing a characterization for the missing critical case. We also investigate the possibility of extensions to the half-space setting. Our observations reveal an interesting half-space phenomenon caused by the unboundedness of the half-space.

KW - Unit ball

KW - Upper half-space

KW - Weighted harmonic bergman spaces

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DO - 10.1016/j.jmaa.2011.02.024

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JO - Journal of Mathematical Analysis and Applications

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ER -

Double integral characterizations of harmonic Bergman spaces

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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