학술논문
Besov–Lipschitz and Mean Besov–Lipschitz Spaces of Holomorphic Functions on the Unit Ball
Document Type
Original Paper
Author
Source
Potential Analysis: An International Journal Devoted to the Interactions between Potential Theory, Probability Theory, Geometry and Functional Analysis. May 2013 38(4):1187-1206
Subject
Language
English
ISSN
0926-2601
1572-929X
1572-929X
Abstract
We give several characterizations of holomorphic mean Besov–Lipschitz spaces on the unit ball in ${\mathbb C^N} $ and appropriate Besov–Lipschitz spaces and prove the equivalences between them. Equivalent norms on the mean Besov–Lipschitz spaces involve different types of Lp -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.