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Composition Operators on Bounded Convex Domains in C-n
- Authors
- Koo, Hyungwoon; Li, Song-Ying
- Issue Date
- 8월-2016
- Publisher
- SPRINGER BASEL AG
- Keywords
- Composition operator; Boundedness; Convex domain; Finite type domain; Smooth symbol
- Citation
- INTEGRAL EQUATIONS AND OPERATOR THEORY, v.85, no.4, pp.555 - 572
- Indexed
- SCIE
SCOPUS
- Journal Title
- INTEGRAL EQUATIONS AND OPERATOR THEORY
- Volume
- 85
- Number
- 4
- Start Page
- 555
- End Page
- 572
- ISSN
- 0378-620X
- Abstract
- We study composition operators on a class of bounded domains including convex domains Omega subset of C-n. We show that a general self-map phi of Omega always induces a bounded operator C-phi : A(alpha)(p)(Omega) -> A(alpha+n-1)(p) (Omega) and the weight gain n - 1 is optimal in certain sense. When phi is smooth, we provide explicit examples which reveal aspects quite different from the strongly pseudoconvex domain setting.
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