For $\lambda\ge0$, a $C^2$ function $f$ defined on the unit disk ${ { \mathbb D}}$ is said to be $\lambda$-analytic if $D_{ \bar{ z}}f=0$, where $D_{ \bar{ z}}$ is the (complex) Dunkl operator given by $D_{ \bar{ z}}f=\partial_{ \bar{ z}}f-\lambda(f(z)-f(\bar{ z}))/(z-\bar{ z})$. The aim of the paper is to study several problems on the associated Bergman spaces $A^{ p}_{ \lambda}({ { \mathbb D}})$ and Hardy spaces $H_{ \lambda}^p({ { \mathbb D}})$ for $p\ge2\lambda/(2\lambda+1)$, such as boundedness of the Bergman projection, growth of functions, density, completeness, and the dual spaces of $A^{ p}_{ \lambda}({ { \mathbb D}})$ and $H_{ \lambda}^p({ { \mathbb D}})$, and characterization and interpolation of $A^{ p}_{ \lambda}({ { \mathbb D}})$.
Categories: math.CV
