Metrical and topological properties of a generalized Libera transform
type: Item
instance of: scholarly article
title: Metrical and topological properties of a generalized Libera transform
zbMATH Open document ID: 0812.30013
DOI: 10.1007/BF01202067
author: Nikolaos Danikas
author: Stephan Ruscheweyh
author: Aristomenis G. Siskakis
published in: Archiv der Mathematik
publication date: 1995-03-19T00:00:00Z
review text: We are identifying subspaces of \({\mathcal H}(\mathbb{D})\) which are preserved under the averaging operator \(\Lambda_{z_ 0}: {\mathcal H}(\mathbb{D})\to {\mathcal H}(\mathbb{D})\) with \[ f\mapsto {1\over z- z_ 0} \int^ z_{z_ 0} f(t) dt, \] where \(z_ 0\in \mathbb{D}\) or, under additional restrictions, \(z_ 0\in \overline{\mathbb{D}}\). Among these subspaces are BMOA, Bloch and Besov spaces of certain types, as well as the spaces of convex respectively close-to-convex univalent functions in \(\mathbb{D}\).
Mathematics Subject Classification ID: 30D55
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 734492
zbMATH Keywords: Bloch functions
zbMATH Keywords: convex univalent functions
zbMATH Keywords: close-to-convex functions
zbMATH Keywords: BMOA
zbMATH Keywords: Besov spaces
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01202067
OpenAlex ID: W2083488426
description: scientific article; zbMATH DE number 734492