Functiones et Approximatio Commentarii Mathematici

Weighted spaces of holomorphic $2\pi$-periodic functions on the upper halfplane

Mohammad Ali Ardalani and Wolfgang Lusky

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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.

Article information

Funct. Approx. Comment. Math., Volume 44, Number 2 (2011), 191-201.

First available in Project Euclid: 22 June 2011

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Zentralblatt MATH identifier

Primary: 46E15: Banach spaces of continuous, differentiable or analytic functions 47B33: Composition operators

weighted spaces holomorphic periodic functions halfplane differentiation operators composition operators


Ardalani, Mohammad Ali; Lusky, Wolfgang. Weighted spaces of holomorphic $2\pi$-periodic functions on the upper halfplane. Funct. Approx. Comment. Math. 44 (2011), no. 2, 191--201. doi:10.7169/facm/1308749123.

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