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A NOTE ON COMPOSITION OPERATORS ACTING ON HOLOMORPHIC SOBOLEV SPACES
- Authors
- Choe, Boo Rim; Koo, Hyungwoon; Smith, Wayne
- Issue Date
- 12월-2011
- Publisher
- AMER MATHEMATICAL SOC
- Keywords
- Composition operator; holomorphic Sobolev spaces; Zygmund class
- Citation
- PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, v.139, no.12, pp.4369 - 4375
- Indexed
- SCIE
SCOPUS
- Journal Title
- PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
- Volume
- 139
- Number
- 12
- Start Page
- 4369
- End Page
- 4375
- ISSN
- 0002-9939
- Abstract
- A holomorphic self-map phi of the unit disk is constructed such that the composition operator induced by phi is bounded on the Hardy-Sobolev space H-2(1) of order 2 as well as on the ordinary holomorphic Lipschitz space Lip(1) but unbounded on the Zygmund class A(1). Among these three function spaces we have embedding relations H-2(1) subset of Lip(1) subset of A(1). So, the main points here are that our construction provides a composition operator which is bounded on smaller spaces, but not on a larger space and that all the function spaces involved are standard ones.
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