Some aspects of the Bergman and Hardy spaces associated with a class of generalized analytic functions

Abstract

For λ≥0, a C2 function f defined on the unit disk D is said to be λ-analytic if Dz̄f=0, where Dz̄ is the (complex) Dunkl operator given by Dz̄f=∂z̄f−λ(f(z)−f(z̄))/(z−z̄). The aim of the paper is to study several problems on the associated Bergman spaces Aλp(D) and Hardy spaces Hλp(D) for p≥2λ/(2λ+1), such as boundedness of the Bergman projection, growth of functions, density, completeness, and the dual spaces of Aλp(D) and Hλp(D), and characterization and interpolation of Aλp(D).