Projections, the weighted bergman spaces, and the bloch space

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

It has been known that there is a family of projections Ps of the Lebesgue spaces onto the Bergman spaces on the unit ball of ℂn(n ≥ 1). The corresponding result for the weighted Bergman spaces Apα is obtained. As applications a solution of Gleason’s problem at the origin for Apa and a characterization of Apα in terms of partial derivatives are indicated without proof. Also the natural limiting case is found: PsL = S, the Bloch space, and PsL = B the PsC0 Bloch space. Moreover, simple bounded linear operators Ls: B →s L B = (A1α)* and B0* = A1α are established under each of pairings suggested by projections Ps.

Original languageEnglish
Pages (from-to)127-136
Number of pages10
JournalProceedings of the American Mathematical Society
Volume108
Issue number1
DOIs
Publication statusPublished - 1990
Externally publishedYes

Fingerprint

Bloch Space
Weighted Bergman Space
Projection
Derivatives
Bergman Space
Lebesgue Space
Partial derivative
Bounded Linear Operator
Unit ball
Pairing
Limiting
Family

Keywords

  • Bloch space
  • Projections
  • Weighted Bergman spaces

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Projections, the weighted bergman spaces, and the bloch space. / Choe, Boo Rim.

In: Proceedings of the American Mathematical Society, Vol. 108, No. 1, 1990, p. 127-136.

Research output: Contribution to journalArticle

@article{8dc21c0c5a9d47b5bc8ef0ef1072817b,
title = "Projections, the weighted bergman spaces, and the bloch space",
abstract = "It has been known that there is a family of projections Ps of the Lebesgue spaces onto the Bergman spaces on the unit ball of ℂn(n ≥ 1). The corresponding result for the weighted Bergman spaces Apα is obtained. As applications a solution of Gleason’s problem at the origin for Apa and a characterization of Apα in terms of partial derivatives are indicated without proof. Also the natural limiting case is found: PsL∞ = S, the Bloch space, and PsL∞ = B the PsC0 Bloch space. Moreover, simple bounded linear operators Ls: B →s L∞ B = (A1α)* and B0* = A1α are established under each of pairings suggested by projections Ps.",
keywords = "Bloch space, Projections, Weighted Bergman spaces",
author = "Choe, {Boo Rim}",
year = "1990",
doi = "10.1090/S0002-9939-1990-0991692-0",
language = "English",
volume = "108",
pages = "127--136",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "1",

}

TY - JOUR

T1 - Projections, the weighted bergman spaces, and the bloch space

AU - Choe, Boo Rim

PY - 1990

Y1 - 1990

N2 - It has been known that there is a family of projections Ps of the Lebesgue spaces onto the Bergman spaces on the unit ball of ℂn(n ≥ 1). The corresponding result for the weighted Bergman spaces Apα is obtained. As applications a solution of Gleason’s problem at the origin for Apa and a characterization of Apα in terms of partial derivatives are indicated without proof. Also the natural limiting case is found: PsL∞ = S, the Bloch space, and PsL∞ = B the PsC0 Bloch space. Moreover, simple bounded linear operators Ls: B →s L∞ B = (A1α)* and B0* = A1α are established under each of pairings suggested by projections Ps.

AB - It has been known that there is a family of projections Ps of the Lebesgue spaces onto the Bergman spaces on the unit ball of ℂn(n ≥ 1). The corresponding result for the weighted Bergman spaces Apα is obtained. As applications a solution of Gleason’s problem at the origin for Apa and a characterization of Apα in terms of partial derivatives are indicated without proof. Also the natural limiting case is found: PsL∞ = S, the Bloch space, and PsL∞ = B the PsC0 Bloch space. Moreover, simple bounded linear operators Ls: B →s L∞ B = (A1α)* and B0* = A1α are established under each of pairings suggested by projections Ps.

KW - Bloch space

KW - Projections

KW - Weighted Bergman spaces

UR - http://www.scopus.com/inward/record.url?scp=84966251834&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966251834&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1990-0991692-0

DO - 10.1090/S0002-9939-1990-0991692-0

M3 - Article

AN - SCOPUS:84966251834

VL - 108

SP - 127

EP - 136

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -