Moment vanishing properties of harmonic Bergman functions

Boo Rim Choe; Hyungwoon Koo; Heungsu Yi

doi:10.1016/j.jmaa.2003.11.005

Moment vanishing properties of harmonic Bergman functions

Boo Rim Choe, Hyungwoon Koo, Heungsu Yi

Department of Mathematics

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

1 Citation (Scopus)

Abstract

We show that Poisson integrals belonging to certain weighted harmonic Bergman spaces b_δ^p on the upper half-space must have the moment vanishing properties. As an application, we show that b₀^p, p≥1, contains a dense subspace whose members have the horizontal moment vanishing properties. Also, we derive related weighted norm inequalities for Poisson integrals. As a consequence, we obtain a characterization for Poisson integrals of continuous functions with compact support in order to belong to b_δ^p.

Original language	English
Pages (from-to)	365-381
Number of pages	17
Journal	Journal of Mathematical Analysis and Applications
Volume	296
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2003.11.005
Publication status	Published - 2004 Aug 15

Keywords

Half-space
Moment vanishing properties
Weighted harmonic Bergman functions

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2003.11.005

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title = "Moment vanishing properties of harmonic Bergman functions",

abstract = "We show that Poisson integrals belonging to certain weighted harmonic Bergman spaces bδp on the upper half-space must have the moment vanishing properties. As an application, we show that b0p, p≥1, contains a dense subspace whose members have the horizontal moment vanishing properties. Also, we derive related weighted norm inequalities for Poisson integrals. As a consequence, we obtain a characterization for Poisson integrals of continuous functions with compact support in order to belong to bδp.",

keywords = "Half-space, Moment vanishing properties, Weighted harmonic Bergman functions",

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

note = "Funding Information: ✩ This research is supported in part by KOSEF(2000-1-10100-001-3) and the Research Grant of Kwangwoon University in 2003. * Corresponding author. E-mail addresses: cbr@korea.ac.kr (B.R. Choe), koohw@korea.ac.kr (H. Koo), hsyi@math.kwangwoon.ac.kr (H. Yi).",

year = "2004",

month = aug,

day = "15",

doi = "10.1016/j.jmaa.2003.11.005",

language = "English",

volume = "296",

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journal = "Journal of Mathematical Analysis and Applications",

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TY - JOUR

T1 - Moment vanishing properties of harmonic Bergman functions

AU - Choe, Boo Rim

AU - Koo, Hyungwoon

AU - Yi, Heungsu

N1 - Funding Information: ✩ This research is supported in part by KOSEF(2000-1-10100-001-3) and the Research Grant of Kwangwoon University in 2003. * Corresponding author. E-mail addresses: cbr@korea.ac.kr (B.R. Choe), koohw@korea.ac.kr (H. Koo), hsyi@math.kwangwoon.ac.kr (H. Yi).

PY - 2004/8/15

Y1 - 2004/8/15

N2 - We show that Poisson integrals belonging to certain weighted harmonic Bergman spaces bδp on the upper half-space must have the moment vanishing properties. As an application, we show that b0p, p≥1, contains a dense subspace whose members have the horizontal moment vanishing properties. Also, we derive related weighted norm inequalities for Poisson integrals. As a consequence, we obtain a characterization for Poisson integrals of continuous functions with compact support in order to belong to bδp.

AB - We show that Poisson integrals belonging to certain weighted harmonic Bergman spaces bδp on the upper half-space must have the moment vanishing properties. As an application, we show that b0p, p≥1, contains a dense subspace whose members have the horizontal moment vanishing properties. Also, we derive related weighted norm inequalities for Poisson integrals. As a consequence, we obtain a characterization for Poisson integrals of continuous functions with compact support in order to belong to bδp.

KW - Half-space

KW - Moment vanishing properties

KW - Weighted harmonic Bergman functions

UR - http://www.scopus.com/inward/record.url?scp=3442893800&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2003.11.005

DO - 10.1016/j.jmaa.2003.11.005

M3 - Article

AN - SCOPUS:3442893800

SN - 0022-247X

VL - 296

SP - 365

EP - 381

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Moment vanishing properties of harmonic Bergman functions

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