Composition as an integral operator
- Authors
- Choe, Boo Rim; Koo, Hyungwoon; Smith, Wayne
- Issue Date
- 19-3월-2015
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Composition operator; Boundedness; Compactness
- Citation
- ADVANCES IN MATHEMATICS, v.273, pp.149 - 187
- Indexed
- SCOPUS
- Journal Title
- ADVANCES IN MATHEMATICS
- Volume
- 273
- Start Page
- 149
- End Page
- 187
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/94107
- DOI
- 10.1016/j.aim.2014.12.022
- ISSN
- 0001-8708
- Abstract
- Let S be the unit sphere and B the unit ball in C-n, and denote by L-1 (S) the usual Lebesgue space of integrable functions on S. We define four "composition operators" acting on L-1 (S) and associated with a Borel function phi : S -> (B) over bar, by first taking one of four natural extensions of f is an element of L-1 (S) to a function on (B) over bar, then composing with phi and taking radial limits. Classical composition operators acting on Hardy spaces of holomorphic functions correspond to a special case. Our main results provide characterizations of when the operators we introduce are bounded or compact on L-t(S), 1 <= t < infinity. Dependence on t and relations between the characterizations for the different operators are also studied. (C) 2014 Elsevier Inc. All rights reserved.
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