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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])
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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

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