Besov-Lipschitz and Mean Besov-Lipschitz Spaces of Holomorphic Functions on the Unit Ball

摘要

We give several characterizations of holomorphic mean Besov-Lipschitz spaces on the unit ball in ?~N and appropriate Besov-Lipschitz spaces and prove the equivalences between them. Equivalent norms on the mean Besov-Lipschitz spaces involve different types of L~p-moduli of continuity, while in characterizations of Hardy-Sobolev spaces we use not only the radial derivative but also the gradient. The characterization in terms of the best approximation by polynomials is also given.