Hölder exponents of Green's functions of Cantor sets
type: Item
instance of: scholarly article
title: Hölder exponents of Green's functions of Cantor sets
zbMATH Open document ID: 1151.31003
DOI: 10.1007/BF03321678
author: Thomas J. Ransford
author: Jérémie Rostand
published in: Computational Methods and Function Theory
publication date: 2008-07-29T00:00:00Z
review text: For \(\tau \in (0,1/2)\), let \(E_{\tau }\) denote the Cantor ternary set with scaling factor \(\tau \). It is known that the Green function \(g\) of \(\mathbb{C}_{\infty }\backslash E_{\tau }\) with pole at \(\infty \) is Hölder continuous of order \(\alpha \) for certain \(\alpha \in (0,1/2]\). This paper obtains improved estimates for \(\alpha \) in terms of \(\tau \). In the classical case where \(\tau =1/3\), it is shown that \(g\) is Hölder continuous of order at least \(0.3413\). The previously known lower bound was \( 0.1898\). The `best' value for \(\alpha \) here remains unknown.
reviewed by: Stephen J. Gardiner
Mathematics Subject Classification ID: 31A15
Mathematics Subject Classification ID: 30C85
Mathematics Subject Classification ID: 65E05
zbMATH DE Number: 5305528
zbMATH Keywords: Hölder continuity
zbMATH Keywords: capacity
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5305528