Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-16T21:48:58.540Z Has data issue: false hasContentIssue false
  • English
  • Français

A property of univalent functions inA_{p}

Published online by Cambridge University Press:  07 August 2001

David Walsh
David Walsh
Affiliation:
Department of Mathematics, NUI Maynooth, Co. Kildare, Ireland
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The univalent functions in the diagonal Besov space A_{p}, where 1<p<\infty , are characterized in terms of the distance from the boundary of a point in the image domain. Here A_{2} is the Dirichlet space. A consequence is that there exist functions in A_{p},\ p>2, for which the area of the complement of the image of the unit disc is zero.

1991 Mathematics Subject Classification 30C99, 46E35.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 42 , Issue 1 , March 2000 , pp. 121 - 124
Copyright
2000 Glasgow Mathematical Journal Trust