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

2011/04/13 by Miroljub Jevtić, Jevtic, M., Miroslav Pavlović +1
Mathematics · #Advanced Harmonic Analysis Research #Holomorphic and Operator Theory #Analytic and geometric function theory

paper · pdf · doi:10.48550/arxiv.1104.2390

Abstract

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.

Related

• Generalized versions of Lipschitz conditions on the modulus of holomorphic functions
• On various approaches to Besov-type spaces of variable smoothness
• Slice regular Besov spaces of hyperholomorphic functions and composition operators
• Linearization of holomorphic Lipschitz functions
• Besov spaces via hyperbolic fillings