Area functions characterizations of weighted Bergman spaces

The aim of this paper is to find weights W   in the unit ball of CnCn for which characterization of the area integrals of Bergman spaces Ap(W)Ap(W) holds. The area functions, related to those used to describe Hardy spaces, involve the radial derivative, the complex gradient and the invariant gradient. We extend to certain Bekollé weights the characterization by Z. Chen and W. Ouyang of the Bergman spaces with the classical weights W(z)=(1−|z|)αW(z)=(1−|z|)α using area functions.