Abstract
We give a characterization for the boundedness of a composition operator on the Bergman space over the two dimensional finite type model domains. For which, we study the boundedness of the composition operators on some singular weighted Bergman space over the two dimensional unit ball. We investigate composition operators on these singular weighted Bergman spaces over the unit ball with smooth symbols, and provide various interesting examples which reveal quite different phenomena from those on the usual weighted Bergman spaces over the unit ball.
| Original language | English |
|---|---|
| Pages (from-to) | 87-114 |
| Number of pages | 28 |
| Journal | Houston Journal of Mathematics |
| Volume | 45 |
| Issue number | 1 |
| Publication status | Published - 2019 |
Bibliographical note
Funding Information:2010 Mathematics Subject Classification. Primary 47B33; Secondary 32A36, 32T25. Key words and phrases. Composition operator, finite type domain, boundedness, smooth symbol. H. Koo was supported by NRF of Korea(2017R1A2B20025).
Funding Information:
H. Koo was supported by NRF of Korea(2017R1A2B20025). Part of this research was performed during the first author’s visit to University of California at Irvine. He thanks the Mathematics Department of University of California at Irvine for its hospitality and support.
Publisher Copyright:
© 2019 University of Houston.
Keywords
- Boundedness
- Composition operator
- Finite type domain
- Smooth symbol
ASJC Scopus subject areas
- General Mathematics