COMPOSITION OPERATORS ON STRICTLY PSEUDOCONVEX DOMAINS WITH SMOOTH SYMBOL
- Authors
- Koo, Hyungwoon; Li, Song-Ying
- Issue Date
- 3월-2014
- Publisher
- PACIFIC JOURNAL MATHEMATICS
- Keywords
- composition operator; strictly pseudoconvex domain; boundedness; smooth symbol
- Citation
- PACIFIC JOURNAL OF MATHEMATICS, v.268, no.1, pp.135 - 153
- Indexed
- SCIE
SCOPUS
- Journal Title
- PACIFIC JOURNAL OF MATHEMATICS
- Volume
- 268
- Number
- 1
- Start Page
- 135
- End Page
- 153
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/99233
- DOI
- 10.2140/pjm.2014.268.135
- ISSN
- 0030-8730
- Abstract
- It is well known that the composition operator C-phi is unbounded on Hardy and Bergman spaces on the unit ball B-n in C-n when n > 1 for a linear holomorphic self-map phi of B-n. We find a sufficient and necessary condition for a composition operator with smooth symbol to be bounded on Hardy or Bergman spaces over a bounded strictly pseudoconvex domain in C-n. Moreover, we show that this condition is equivalent to the compactness of the composition operator from a Hardy or Bergman space into the Bergman space whose weight is 1/4 bigger. We also prove that a certain jump phenomenon occurs when the composition operator is not bounded. Our results generalize known results on the unit ball to strictly pseudoconvex domains.
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