Projections for harmonic Bergman spaces and applications

Boo Rim Choe; Hyungwoon Koo; Heungsu Yi

doi:10.1016/j.jfa.2004.02.014

Projections for harmonic Bergman spaces and applications

Boo Rim Choe, Hyungwoon Koo, Heungsu Yi

Department of Mathematics

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

7 Citations (Scopus)

Abstract

On the setting of general bounded smooth domains in Rⁿ, we construct L¹-bounded nonorthogonal projections and obtain related reproducing formulas for the harmonic Bergman spaces. In addition, we show that those projections satisfy Sobolev L^p -estimates of any order even for p=1. Among applications are Gleason's problems for the harmonic Bergman-Sobolev and (little) Bloch functions on star-shaped domains with strong reference points.

Original language	English
Pages (from-to)	388-421
Number of pages	34
Journal	Journal of Functional Analysis
Volume	216
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2004.02.014
Publication status	Published - 2004 Nov 15

Keywords

Gleason's problem
Harmonic Bergman function
Projection

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2004.02.014

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title = "Projections for harmonic Bergman spaces and applications",

abstract = "On the setting of general bounded smooth domains in Rn, we construct L1-bounded nonorthogonal projections and obtain related reproducing formulas for the harmonic Bergman spaces. In addition, we show that those projections satisfy Sobolev Lp -estimates of any order even for p=1. Among applications are Gleason's problems for the harmonic Bergman-Sobolev and (little) Bloch functions on star-shaped domains with strong reference points.",

keywords = "Gleason's problem, Harmonic Bergman function, Projection",

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

note = "Funding Information: ·Corresponding author. E-mail addresses: cbr@korea.ac.kr (B.R. Choe), koohw@korea.ac.kr (H. Koo), hsyi@ kwangwoon.ac.kr (H. Yi). 1Supported by KOSEF(R01-2003-000-10243-0). 2Supported by the research grant of Kwangwoon University (2004).",

year = "2004",

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doi = "10.1016/j.jfa.2004.02.014",

language = "English",

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T1 - Projections for harmonic Bergman spaces and applications

AU - Choe, Boo Rim

AU - Koo, Hyungwoon

AU - Yi, Heungsu

N1 - Funding Information: ·Corresponding author. E-mail addresses: cbr@korea.ac.kr (B.R. Choe), koohw@korea.ac.kr (H. Koo), hsyi@ kwangwoon.ac.kr (H. Yi). 1Supported by KOSEF(R01-2003-000-10243-0). 2Supported by the research grant of Kwangwoon University (2004).

PY - 2004/11/15

Y1 - 2004/11/15

N2 - On the setting of general bounded smooth domains in Rn, we construct L1-bounded nonorthogonal projections and obtain related reproducing formulas for the harmonic Bergman spaces. In addition, we show that those projections satisfy Sobolev Lp -estimates of any order even for p=1. Among applications are Gleason's problems for the harmonic Bergman-Sobolev and (little) Bloch functions on star-shaped domains with strong reference points.

AB - On the setting of general bounded smooth domains in Rn, we construct L1-bounded nonorthogonal projections and obtain related reproducing formulas for the harmonic Bergman spaces. In addition, we show that those projections satisfy Sobolev Lp -estimates of any order even for p=1. Among applications are Gleason's problems for the harmonic Bergman-Sobolev and (little) Bloch functions on star-shaped domains with strong reference points.

KW - Gleason's problem

KW - Harmonic Bergman function

KW - Projection

UR - http://www.scopus.com/inward/record.url?scp=4344582748&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2004.02.014

DO - 10.1016/j.jfa.2004.02.014

M3 - Article

AN - SCOPUS:4344582748

SN - 0022-1236

VL - 216

SP - 388

EP - 421

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

Projections for harmonic Bergman spaces and applications

Abstract

Keywords

ASJC Scopus subject areas

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