Gleason's problem for harmonic Bergman and Bloch functions on half-spaces

Boo Rim Choe; Hyungwoon Koo; Heungsu Yi

doi:10.1007/BF01213925

Gleason's problem for harmonic Bergman and Bloch functions on half-spaces

Boo Rim Choe, Hyungwoon Koo, Heungsu Yi

Department of Mathematics

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

8 Citations (Scopus)

Abstract

On the setting of the half-space R^n-1 × R₊, we investigate Gleason's problem for harmonic Bergman and Bloch functions. We prove that Gleason's problem for the harmonic L^p-Bergman space is solvable if and only if p > n. We also prove that Gleason's problem for the harmonic (little) Bloch space is solvable.

Original language	English
Pages (from-to)	269-287
Number of pages	19
Journal	Integral Equations and Operator Theory
Volume	36
Issue number	3
DOIs	https://doi.org/10.1007/BF01213925
Publication status	Published - 2000 Mar

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/BF01213925

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title = "Gleason's problem for harmonic Bergman and Bloch functions on half-spaces",

abstract = "On the setting of the half-space Rn-1 × R+, we investigate Gleason's problem for harmonic Bergman and Bloch functions. We prove that Gleason's problem for the harmonic Lp-Bergman space is solvable if and only if p > n. We also prove that Gleason's problem for the harmonic (little) Bloch space is solvable.",

author = "Choe, {Boo Rim} and Hyungwoon Koo and Heungsu Yi",

note = "Funding Information: Acknowledgement. The first author is partially supported by GARC(98) and KOSEF (98-0701-03-01-5). The second author is partially supported by KOSEF(981-0102-009-2). The third author wishes to acknowledge the financial support of the Korea Research Foundation made in the program year of 1997-1998.",

year = "2000",

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AU - Choe, Boo Rim

AU - Koo, Hyungwoon

AU - Yi, Heungsu

N1 - Funding Information: Acknowledgement. The first author is partially supported by GARC(98) and KOSEF (98-0701-03-01-5). The second author is partially supported by KOSEF(981-0102-009-2). The third author wishes to acknowledge the financial support of the Korea Research Foundation made in the program year of 1997-1998.

PY - 2000/3

Y1 - 2000/3

N2 - On the setting of the half-space Rn-1 × R+, we investigate Gleason's problem for harmonic Bergman and Bloch functions. We prove that Gleason's problem for the harmonic Lp-Bergman space is solvable if and only if p > n. We also prove that Gleason's problem for the harmonic (little) Bloch space is solvable.

AB - On the setting of the half-space Rn-1 × R+, we investigate Gleason's problem for harmonic Bergman and Bloch functions. We prove that Gleason's problem for the harmonic Lp-Bergman space is solvable if and only if p > n. We also prove that Gleason's problem for the harmonic (little) Bloch space is solvable.

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U2 - 10.1007/BF01213925

DO - 10.1007/BF01213925

M3 - Article

AN - SCOPUS:0013275359

SN - 0378-620X

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SP - 269

EP - 287

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 3

ER -

Gleason's problem for harmonic Bergman and Bloch functions on half-spaces

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