Composition operators acting on holomorphic Sobolev spaces

Boo Rim Choe; Hyungwoon Koo; Wayne Smith

doi:10.1090/S0002-9947-03-03273-2

Composition operators acting on holomorphic Sobolev spaces

Boo Rim Choe, Hyungwoon Koo, Wayne Smith

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

12 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 language	English
Pages (from-to)	2829-2855
Number of pages	27
Journal	Transactions of the American Mathematical Society
Volume	355
Issue number	7
DOIs	https://doi.org/10.1090/S0002-9947-03-03273-2
Publication status	Published - 2003 Jul

Keywords

Bergman space
Composition operator
Fractional derivative

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1090/S0002-9947-03-03273-2

Cite this

@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 Hyungwoon Koo and Wayne Smith",

year = "2003",

month = jul,

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, Hyungwoon

AU - Smith, Wayne

PY - 2003/7

Y1 - 2003/7

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

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

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

M3 - Article

AN - SCOPUS:0037790976

SN - 0002-9947

VL - 355

SP - 2829

EP - 2855

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 7

ER -

Composition operators acting on holomorphic Sobolev spaces

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this