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://ucrisportal.univie.ac.at/en/publications/duality-and-approximation-of-bergman-spaces(7699841e-472f-4b5f-90a9-6d533b141116).html