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AN INTEGRAL REPRESENTATION FOR BESOV AND LIPSCHITZ SPACES
Published online by Cambridge University Press: 17 October 2014
Abstract
It is well known that functions in the analytic Besov space $B_{1}$ on the unit disk
$\mathbb{D}$ admit an integral representation
$$\begin{eqnarray}f(z)=\int _{\mathbb{D}}\frac{z-w}{1-z\overline{w}}\,d{\it\mu}(w),\end{eqnarray}$$
${\it\mu}$ is a complex Borel measure with
$|{\it\mu}|(\mathbb{D})<\infty$. 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.
Keywords
MSC classification
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 98 , Issue 1 , February 2015 , pp. 129 - 144
- Copyright
- Copyright © 2014 Australian Mathematical Publishing Association Inc.
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