Duality and approximation of Bergman spaces

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.

References in corpus (4)

• The Bergman projection on fat Hartogs triangles: L^p boundedness
• Bergman subspaces and subkernels: Degenerate $L^p$ mapping and zeroes
• Irregularity of the Bergman projection on worm domains in C^n
• Bergman theory of certain generalized Hartogs triangles

Cited by in corpus (6)

• $L^p$-regularity of the Bergman projection on quotient domains
• Bergman Kernels of Elementary Reinhardt Domains
• Sobolev mapping of some holomorphic projections
• Projections onto $L^p$-Bergman spaces of Reinhardt Domains
• Hardy Spaces for a Class of Singular Domains
• Product domains, Multi-Cauchy transforms, and the $\bar{\partial }$ equation