Area functions characterizations of weighted Bergman spaces and area operators

We completely characterize the boundedness and compactness of the area operators on weighted Bergman spaces Ap(ω) over the unit ball induced by Békollé weights. Using the characterization of the boundedness, we obtain some general area formulas in terms of the radial derivative, the complex gradient, and the invariant gradient for Ap(ω). As an application of area operator and the general area formula related to the radial derivative, we characterize the boundedness and compactness of Volterra integral operators.