Abstract
In this paper, we study the composition operator CΦ with a smooth but not necessarily holomorphic symbol Φ. A necessary and sufficient condition on Φ for CΦ to be bounded on holomorphic (respectively harmonic) weighted Bergman spaces of the unit ball in Cn (respectively Rn) is given. The condition is a real version of Wogen's condition for the holomorphic spaces, and a non-vanishing boundary Jacobian condition for the harmonic spaces. We also show certain jump phenomena on the weights for the target spaces for both the holomorphic and harmonic spaces.
Original language | English |
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Pages (from-to) | 2747-2767 |
Number of pages | 21 |
Journal | Journal of Functional Analysis |
Volume | 256 |
Issue number | 9 |
DOIs | |
Publication status | Published - 2009 May 1 |
Bibliographical note
Funding Information:✩ Koo is partially supported by the KRF-2008-314-C00012 and Wang is partially supported by the NSF-10671147 and NSF-10571044 of China. * Corresponding author. E-mail addresses: [email protected] (H. Koo), [email protected] (M. Wang).
Keywords
- Bergman space
- Boundedness
- Carleson measure
- Composition operator
- Smooth map
- Unit ball
ASJC Scopus subject areas
- Analysis