Maximal and Area Integral Characterizations of Bergman Spaces in the Unit Ball of ℂn

Abstract EN

We present maximal and area integral characterizations of Bergman spaces in the unit ball of ℂn.

The characterizations are in terms of maximal functions and area integral functions on Bergman balls involving the radial derivative, the complex gradient, and the invariant gradient.

As an application, we obtain new maximal and area integral characterizations of Besov spaces.

Moreover, we give an atomic decomposition of real-variable type with respect to Carleson tubes for Bergman spaces.