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Composition operators on holomorphic Sobolev spaces in B-n
- Authors
- Koo, Hyungwoon; Park, Inyoung
- Issue Date
- 1-9월-2010
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Composition operator; Boundedness; Compactness; Holomorphic Sobolev space; Unit ball
- Citation
- JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.369, no.1, pp.232 - 244
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
- Volume
- 369
- Number
- 1
- Start Page
- 232
- End Page
- 244
- ISSN
- 0022-247X
- Abstract
- We study the composition operator C-Phi on holomorphic Sobolev spaces induced by an analytic self-map Phi of B-n in C-n that extends to be smooth on (B) over bar (n). We characterize the boundedness and the compactness of C-Phi on A(alpha,s)(p), and prove the jump phenomenon of C-Phi on A(alpha,s)(p). moreover, we show an interesting result that the boundedness of C-Phi on A(alpha,s)(p) is equivalent to the compactness of C-Phi : A(alpha,s)(p) -> A(beta,t)(q) for appropriate A(beta,t)(q), for example A(beta,t)(q) = A(alpha+1/4,s)(p). We provide examples to show that our results are sharp. (C) 2010 Elsevier Inc. All rights reserved.
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