Abstract
We study the composition operator CΦ on holomorphic Sobolev spaces induced by an analytic self-map Φ of Bn in Cn that extends to be smooth on Bn. We characterize the boundedness and the compactness of CΦ on Aα,sp, and prove the jump phenomenon of CΦ on Aα,sp. Moreover, we show an interesting result that the boundedness of CΦ on Aα,sp is equivalent to the compactness of CΦ:Aα,sp→Aβ,tq for appropriate Aβ,tq, for example Aβ,tq=Aα+1/4,sp. We provide examples to show that our results are sharp.
Original language | English |
---|---|
Pages (from-to) | 232-244 |
Number of pages | 13 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 369 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2010 Sept |
Keywords
- Boundedness
- Compactness
- Composition operator
- Holomorphic Sobolev space
- Unit ball
ASJC Scopus subject areas
- Analysis
- Applied Mathematics