Duality and approximation of Bergman spaces
Complex Variables
2018-11-16 v2
Abstract
Expected duality and approximation properties are shown to fail on Bergman spaces of domains in , 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.
Keywords
Cite
@article{arxiv.1804.02746,
title = {Duality and approximation of Bergman spaces},
author = {D. Chakrabarti and L. D. Edholm and J. D. McNeal},
journal= {arXiv preprint arXiv:1804.02746},
year = {2018}
}