Abstract
We introduce the scale of weighted Bergman spaces on hyperconvex domains in ℂn and use the Lelong-Jensen formula to prove some fundamental results about these spaces. In particular, generalizations of such classical results as the Littlewood subordination principle, the Littlewood-Paley identity and the change of variables formula are proven. Geometric properties of the introduced norms are revealed by the Nevanlinna counting function associated with a chosen exhaustion. In the last several sections we prove boundedness and compactness results for composition operators generated by holomorphic mappings of hyperconvex domains.
Original language | English (US) |
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Pages (from-to) | 2153-2201 |
Number of pages | 49 |
Journal | Indiana University Mathematics Journal |
Volume | 57 |
Issue number | 5 |
DOIs | |
State | Published - 2008 |
Keywords
- Composition operators
- Pluripotential theory
- Plurisubharmonic functions
ASJC Scopus subject areas
- General Mathematics