A Derivative-Free Characterization of the Weighted Besov Spaces

Abstract

We obtain a characterization of the weighted Besov space \({{\cal B}_K}\left( p \right)\) for a weight function K, 0 < p < ∞, in terms of symmetric and derivative-free double integrals with the weight function K in the unit disc. As a by-product, we give a modification of the identity of Littlewood—Paley type for the Bergman space. As an application, a derivative-free characterization of \({{\cal Q}_K}\) type spaces is obtained.