Univalent functions in Hardy spaces in terms of the growth of arc-length
type: Item
instance of: scholarly article
title: Univalent functions in Hardy spaces in terms of the growth of arc-length
zbMATH Open document ID: 1206.30077
author: Cristóbal González
author: José Ángel Peláez
published in: The Journal of Geometric Analysis
publication date: 2009-11-02T00:00:00Z
review text: Pommerenke proved in 1962 that for \(f\) univalent in the unit disk and \(0<p<2\), \(f\in H^p\) if and only if \[ \int_0^1M_1^p(r,f')\,dr < \infty. \] In this paper, the authors prove that this result continues to be true for \(p\) strictly larger than \(2\), but is false for large \(p\). In addition, it turns out that the result is true for all \(p\) when \(f\) is restricted to the class of close-to-convex functions. Finally, the authors discuss the membership of univalent functions in some related spaces of Dirichlet type.
Mathematics Subject Classification ID: 30H10
Mathematics Subject Classification ID: 30C55
zbMATH DE Number: 5624077
zbMATH Keywords: univalent function
zbMATH Keywords: Hardy space
zbMATH Keywords: integral means
zbMATH Keywords: arc-length
zbMATH Keywords: Dirichlet type spaces
reviewed by: Martin Chuaqui
MaRDI profile type: Publication
full work available at URL: s12220-009-9092-9
OpenAlex ID: W2126360210
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DOI: 10.1007/S12220-009-9092-9
description: scientific article; zbMATH DE number 5624077