Composition Operators on Bounded Convex Domains in Cn

Hyungwoon Koo; Song Ying Li

doi:10.1007/s00020-016-2300-7

Composition Operators on Bounded Convex Domains in Cⁿ

Hyungwoon Koo^*, Song Ying Li

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

We study composition operators on a class of bounded domains including convex domains Ω ⊂ Cⁿ. We show that a general self-map ϕ of Ω always induces a bounded operator Cϕ:Aαp(Ω)→Aα+n-1p(Ω) and the weight gain n- 1 is optimal in certain sense. When ϕ is smooth, we provide explicit examples which reveal aspects quite different from the strongly pseudoconvex domain setting.

Original language	English
Pages (from-to)	555-572
Number of pages	18
Journal	Integral Equations and Operator Theory
Volume	85
Issue number	4
DOIs	https://doi.org/10.1007/s00020-016-2300-7
Publication status	Published - 2016 Aug 1

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing.

Keywords

Boundedness
Composition operator
Convex domain
Finite type domain
Smooth symbol

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

Access to Document

10.1007/s00020-016-2300-7

Cite this

@article{9b12f4494dc64312a9485509619c434b,

title = "Composition Operators on Bounded Convex Domains in Cn ",

abstract = "We study composition operators on a class of bounded domains including convex domains Ω ⊂ Cn. We show that a general self-map ϕ of Ω always induces a bounded operator Cϕ:Aαp(Ω)→Aα+n-1p(Ω) and the weight gain n- 1 is optimal in certain sense. When ϕ is smooth, we provide explicit examples which reveal aspects quite different from the strongly pseudoconvex domain setting.",

keywords = "Boundedness, Composition operator, Convex domain, Finite type domain, Smooth symbol",

author = "Hyungwoon Koo and Li, \{Song Ying\}",

note = "Publisher Copyright: {\textcopyright} 2016, Springer International Publishing.",

year = "2016",

month = aug,

day = "1",

doi = "10.1007/s00020-016-2300-7",

language = "English",

volume = "85",

pages = "555--572",

journal = "Integral Equations and Operator Theory",

issn = "0378-620X",

publisher = "Birkhauser Verlag Basel",

number = "4",

}

TY - JOUR

T1 - Composition Operators on Bounded Convex Domains in Cn

AU - Koo, Hyungwoon

AU - Li, Song Ying

PY - 2016/8/1

Y1 - 2016/8/1

N2 - We study composition operators on a class of bounded domains including convex domains Ω ⊂ Cn. We show that a general self-map ϕ of Ω always induces a bounded operator Cϕ:Aαp(Ω)→Aα+n-1p(Ω) and the weight gain n- 1 is optimal in certain sense. When ϕ is smooth, we provide explicit examples which reveal aspects quite different from the strongly pseudoconvex domain setting.

AB - We study composition operators on a class of bounded domains including convex domains Ω ⊂ Cn. We show that a general self-map ϕ of Ω always induces a bounded operator Cϕ:Aαp(Ω)→Aα+n-1p(Ω) and the weight gain n- 1 is optimal in certain sense. When ϕ is smooth, we provide explicit examples which reveal aspects quite different from the strongly pseudoconvex domain setting.

KW - Boundedness

KW - Composition operator

KW - Convex domain

KW - Finite type domain

KW - Smooth symbol

UR - https://www.scopus.com/pages/publications/84968662187

U2 - 10.1007/s00020-016-2300-7

DO - 10.1007/s00020-016-2300-7

M3 - Article

AN - SCOPUS:84968662187

SN - 0378-620X

VL - 85

SP - 555

EP - 572

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 4

ER -