Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-01-12T19:05:15.656Z Has data issue: false hasContentIssue false
  • English
  • Français

Boundedness of the Cesàro averaging operators on Dirichlet spaces

Published online by Cambridge University Press:  12 July 2007

Kenneth F. Andersen
Kenneth F. Andersen
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that the Cesàro averaging operators Cα, Re α > −1, introduced by Stempak, are bounded on the Dirichlet space Da if and only if a > 0, while the associated operators Aα are bounded on Da if and only if −1 < a < 2. This extends results of Galanopoulos, who considered the particular case α = 0 for 0 ≤ a ≤ 1.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 4 , August 2004 , pp. 609 - 616
Copyright
Copyright © Royal Society of Edinburgh 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)