Composition operators acting on holomorphic Sobolev spaces

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We study the action of composition operators on Sobolev spaces of analytic functions having fractional derivatives in some weighted Bergman space or Hardy space on the unit disk. Criteria for when such operators are bounded or compact are given. In particular, we find the precise range of orders of fractional derivatives for which all composition operators are bounded on such spaces. Sharp results about boundedness and compactness of a composition operator are also given when the inducing map is polygonal.

Original languageEnglish
Pages (from-to)2829-2855
Number of pages27
JournalTransactions of the American Mathematical Society
Volume355
Issue number7
DOIs
Publication statusPublished - 2003 Jul 1

Fingerprint

Sobolev spaces
Composition Operator
Sobolev Spaces
Mathematical operators
Fractional Derivative
Chemical analysis
Derivatives
Weighted Bergman Space
Space of Analytic Functions
Hardy Space
Unit Disk
Compactness
Boundedness
Operator
Range of data

Keywords

  • Bergman space
  • Composition operator
  • Fractional derivative

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Composition operators acting on holomorphic Sobolev spaces. / Choe, Boo Rim; Koo, Hyung Woon; Smith, Wayne.

In: Transactions of the American Mathematical Society, Vol. 355, No. 7, 01.07.2003, p. 2829-2855.

Research output: Contribution to journalArticle

@article{6735cf02526a4e58a3846628715ba1e9,
title = "Composition operators acting on holomorphic Sobolev spaces",
abstract = "We study the action of composition operators on Sobolev spaces of analytic functions having fractional derivatives in some weighted Bergman space or Hardy space on the unit disk. Criteria for when such operators are bounded or compact are given. In particular, we find the precise range of orders of fractional derivatives for which all composition operators are bounded on such spaces. Sharp results about boundedness and compactness of a composition operator are also given when the inducing map is polygonal.",
keywords = "Bergman space, Composition operator, Fractional derivative",
author = "Choe, {Boo Rim} and Koo, {Hyung Woon} and Wayne Smith",
year = "2003",
month = "7",
day = "1",
doi = "10.1090/S0002-9947-03-03273-2",
language = "English",
volume = "355",
pages = "2829--2855",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "7",

}

TY - JOUR

T1 - Composition operators acting on holomorphic Sobolev spaces

AU - Choe, Boo Rim

AU - Koo, Hyung Woon

AU - Smith, Wayne

PY - 2003/7/1

Y1 - 2003/7/1

N2 - We study the action of composition operators on Sobolev spaces of analytic functions having fractional derivatives in some weighted Bergman space or Hardy space on the unit disk. Criteria for when such operators are bounded or compact are given. In particular, we find the precise range of orders of fractional derivatives for which all composition operators are bounded on such spaces. Sharp results about boundedness and compactness of a composition operator are also given when the inducing map is polygonal.

AB - We study the action of composition operators on Sobolev spaces of analytic functions having fractional derivatives in some weighted Bergman space or Hardy space on the unit disk. Criteria for when such operators are bounded or compact are given. In particular, we find the precise range of orders of fractional derivatives for which all composition operators are bounded on such spaces. Sharp results about boundedness and compactness of a composition operator are also given when the inducing map is polygonal.

KW - Bergman space

KW - Composition operator

KW - Fractional derivative

UR - http://www.scopus.com/inward/record.url?scp=0037790976&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037790976&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-03-03273-2

DO - 10.1090/S0002-9947-03-03273-2

M3 - Article

AN - SCOPUS:0037790976

VL - 355

SP - 2829

EP - 2855

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 7

ER -