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June 2011 Weighted spaces of holomorphic $2\pi$-periodic functions on the upper halfplane
Mohammad Ali Ardalani, Wolfgang Lusky
Funct. Approx. Comment. Math. 44(2): 191-201 (June 2011). DOI: 10.7169/facm/1308749123

Abstract

We consider spaces of $2\pi$-periodic holomorphic functions $f$ on the upper halfplane $G$ which are bounded by a~weighted sup-norm $\sup_{w \in G} |f(w)|v(w)$. Here $v: G \rightarrow ]0, \infty[$ is a function which depends essentially only on $Im(w)$, $w \in G$, and satisfies $ \lim_{t \rightarrow 0} v(it) =0$. We give a complete isomorphic classification of such spaces and investigate composition operators and the differentiation operator between them.

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Mohammad Ali Ardalani. Wolfgang Lusky. "Weighted spaces of holomorphic $2\pi$-periodic functions on the upper halfplane." Funct. Approx. Comment. Math. 44 (2) 191 - 201, June 2011. https://doi.org/10.7169/facm/1308749123

Information

Published: June 2011
First available in Project Euclid: 22 June 2011

zbMATH: 1242.46030
MathSciNet: MR2841178
Digital Object Identifier: 10.7169/facm/1308749123

Subjects:
Primary: ‎46E15 , 47B33

Keywords: Composition operators , differentiation operators , halfplane , holomorphic periodic functions , weighted spaces

Rights: Copyright © 2011 Adam Mickiewicz University

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Vol.44 • No. 2 • June 2011
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