Abstract
It is well known that the composition operator CΦ is unbounded on Hardy and Bergman spaces on the unit ball Bn in ℂn when n > 1 for a linear holomorphic self-map Φ of Bn. 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 ℂn. 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.
Original language | English |
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Pages (from-to) | 135-153 |
Number of pages | 19 |
Journal | Pacific Journal of Mathematics |
Volume | 268 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2014 |
Keywords
- Boundedness
- Composition operator
- Smooth symbol
- Strictly pseudoconvex domain
ASJC Scopus subject areas
- Mathematics(all)