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arXiv · 1101.2995

An integral representation for Besov and Lipschitz spaces

Kehe Zhu
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Abstract

It is well known that functions in the analytic Besov space $B_1$ on the unit disk $\D$ admits an integral representation $$f(z)=\ind\frac{z-w}{1-z\bar w}\,d\mu(w),$$ where $\mu$ is a complex Borel measure with $|\mu|(\D)<\infty$. We generalize this result to all Besov spaces $B_p$ with $0 1$. We also obtain a version for Bergman and Fock spaces.

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Kehe Zhu. 2011-01-15. An integral representation for Besov and Lipschitz spaces. https://doi.org/10.1017/s1446788714000469

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