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- Title
AN INTEGRAL REPRESENTATION FOR BESOV AND LIPSCHITZ SPACES.
- Authors
ZHU, KEHE
- Abstract
It is well known that functions in the analytic Besov space $B_{1}$ on the unit disk $\mathbb{D}$ admit an integral representation $$\begin{eqnarray}f(z)=\int _{\mathbb{D}}\frac{z-w}{1-z\overline{w}}\,d{\it\mu}(w),\end{eqnarray}$$ where ${\it\mu}$ is a complex Borel measure with $<INNOPIPE>{\it\mu}<INNOPIPE>(\mathbb{D})<\infty$. We generalize this result to all Besov spaces $B_{p}$ with $0<p\leq 1$ and all Lipschitz spaces ${\rm\Lambda}_{t}$ with $t>1$. We also obtain a version for Bergman and Fock spaces.
- Subjects
BESOV spaces; LIPSCHITZ spaces; BOREL subsets; INTEGRAL representations; FOCK spaces
- Publication
Journal of the Australian Mathematical Society, 2015, Vol 98, Issue 1, p129
- ISSN
1446-7887
- Publication type
Article
- DOI
10.1017/S1446788714000469