Duality and approximation of Bergman spaces

Abstract

Expected duality and approximation properties are shown to fail on Bergman spaces of domains in Cn, 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.