Bounded operators on the weighted spaces of holomorphic functions on the unit ball in $C^n$

A. V. Harutyunyan; W. Lusky

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arXiv · 1407.0072

Bounded operators on the weighted spaces of holomorphic functions on the unit ball in $C^n$

A. V. Harutyunyan·W. Lusky

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Abstract

Assuming that $S$ is the space of functions of regular variation, $ω\in S$, $0< p<\infty$, a function $f$ holomorphic in $B^n$ is said to be of Besov space $B_p(ω)$ if $$\|f\|^p_{B_p(ω)}=\int_{B^n} (1-|z|^2)^p|Df(z)|^p\frac{ω(1-|z|)}{(1-|z|^2)^{n+1}}dν(z) <+\infty,$$ where $dν(z) $ is the volume measure on $B^n$ and $D $ stands for a fractional derivative of $f$. We consider operators on $B_p(ω)$ and show, that they are bounded.

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BibTeX RIS

A. V. Harutyunyan, W. Lusky. 2014-06-30. Bounded operators on the weighted spaces of holomorphic functions on the unit ball in $C^n$. https://arxiv.org/abs/1407.0072

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