Duality and approximation of Bergman spaces
- Author(s)
- Luke David Edholm, Jeffery D. McNeal, Debraj Chakrabarti
- Abstract
Expected duality and approximation properties are shown to fail on Bergman spaces of domains in C
n, via examples. When the domain admits an operator satisfying certain mapping properties, positive duality and approximation results are proved. Such operators are constructed on generalized Hartogs triangles. On a general bounded Reinhardt domain, norm convergence of Laurent series of Bergman functions is shown. This extends a classical result on Hardy spaces of the unit disc.
- Organisation(s)
- Department of Mathematics
- External organisation(s)
- Ohio State University, Central Michigan University
- Journal
- Advances in Mathematics
- Volume
- 341
- Pages
- 616-656
- No. of pages
- 41
- ISSN
- 0001-8708
- DOI
- https://doi.org/10.1016/j.aim.2018.10.041
- Publication date
- 01-2019
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101008 Complex analysis
- Keywords
- ASJC Scopus subject areas
- Mathematics(all)
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/duality-and-approximation-of-bergman-spaces(7699841e-472f-4b5f-90a9-6d533b141116).html