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

Department of Mathematics

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

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

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KW - Finite type domain

KW - Smooth symbol

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