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arXiv · 1804.02746

Duality and approximation of Bergman spaces

D. Chakrabarti·L. D. Edholm·J. D. McNeal
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Abstract

Expected duality and approximation properties are shown to fail on Bergman spaces of domains in $\mathbb{C}^n$, 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.

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D. Chakrabarti, L. D. Edholm, J. D. McNeal. 2018-04-08. Duality and approximation of Bergman spaces. https://doi.org/10.1016/j.aim.2018.10.041

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