Besov-Lipschitz and mean Besov-Lipschitz spaces of holomorphic functions on the unit ball

Details Besov-Lipschitz and mean Besov-Lipschitz spaces of holomorphic functions on the unit ball Besov-Lipschitz and mean Besov-Lipschitz spaces of holomorphic functions on the unit ball

2011-04-13

arxiv.org/abs/1104.2390v1

Mathematics

Complex Variables

Scientific paper

We give several characterizations of holomorphic mean Besov-Lipschitz space on the unit ball in $\cn $ and appropriate Besov-Lipschitz space and prove the equivalences between them. Equivalent norms on the mean Besov-Lipschitz space involve different types of $L^p$-moduli of continuity, while in characterizations of Besov-Lipschitz space we use not only the radial derivative but also the gradient and the tangential derivatives. The characterization in terms of the best approximation by polynomials is also given.

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