The ∂-complex on weighted Bergman spaces on Hermitian manifolds
- Author(s)
- Duong Ngoc Son, Friedrich Haslinger
- Abstract
In this paper, we investigate the ∂-complex on weighted Bergman spaces on Hermitian manifolds satisfying a certain holomorphicity/duality condition. This generalizes the situation of the Segal-Bargmann space in Cn, studied earlier by the first-named author, in which the adjoint of the differentiation is the multiplication by z. The results are applied to two important examples in the unit ball, namely, the complex hyperbolic metric and a conformally Kähler metric which are related to Bergman spaces with so-called “exponential” and “standard” weights, respectively. In particular, we obtain new estimates for the solutions of the ∂-quation on these weighted Bergman spaces.
- Organisation(s)
- Department of Mathematics
- Journal
- Journal of Mathematical Analysis and Applications
- Volume
- 487
- No. of pages
- 25
- ISSN
- 0022-247X
- DOI
- https://doi.org/10.1016/j.jmaa.2020.123994
- Publication date
- 07-2020
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101008 Complex analysis
- Keywords
- ASJC Scopus subject areas
- Analysis, Applied Mathematics
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/5fb09c97-1868-454c-a1d0-76ea41a10787