Derivatives of Harmonic Bergman and Bloch Functions on the Ball

Boo Rim Choe; Hyungwoon Koo; Heungsu Yi

doi:10.1006/jmaa.2000.7438

Derivatives of Harmonic Bergman and Bloch Functions on the Ball

Boo Rim Choe, Hyungwoon Koo, Heungsu Yi

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

24 Citations (Scopus)

Abstract

On the setting of the unit ball of euclidean n-space, we investigate properties of derivatives of functions in the harmonic Bergman space and the harmonic Bloch space. Our results are (1) size estimates of derivatives of the harmonic Bergman kernel, (2) Gleason's problem, and (3) characterizations in terms of radial, tangential, and ordinary derivative norms. In the course of proofs, some reproducing formulas are found and estimated.

Original language	English
Pages (from-to)	100-123
Number of pages	24
Journal	Journal of Mathematical Analysis and Applications
Volume	260
Issue number	1
DOIs	https://doi.org/10.1006/jmaa.2000.7438
Publication status	Published - 2001 Aug 1

Bibliographical note

Funding Information:
This research is partially supported by the Korea Research Foundation Grant (KRF-1999-015-DI0005).

Keywords

Harmonic Bergman and Bloch functions; Gleason's problem; derivative norms

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1006/jmaa.2000.7438

Cite this

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abstract = "On the setting of the unit ball of euclidean n-space, we investigate properties of derivatives of functions in the harmonic Bergman space and the harmonic Bloch space. Our results are (1) size estimates of derivatives of the harmonic Bergman kernel, (2) Gleason's problem, and (3) characterizations in terms of radial, tangential, and ordinary derivative norms. In the course of proofs, some reproducing formulas are found and estimated.",

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AU - Yi, Heungsu

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N2 - On the setting of the unit ball of euclidean n-space, we investigate properties of derivatives of functions in the harmonic Bergman space and the harmonic Bloch space. Our results are (1) size estimates of derivatives of the harmonic Bergman kernel, (2) Gleason's problem, and (3) characterizations in terms of radial, tangential, and ordinary derivative norms. In the course of proofs, some reproducing formulas are found and estimated.

AB - On the setting of the unit ball of euclidean n-space, we investigate properties of derivatives of functions in the harmonic Bergman space and the harmonic Bloch space. Our results are (1) size estimates of derivatives of the harmonic Bergman kernel, (2) Gleason's problem, and (3) characterizations in terms of radial, tangential, and ordinary derivative norms. In the course of proofs, some reproducing formulas are found and estimated.

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Derivatives of Harmonic Bergman and Bloch Functions on the Ball

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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