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The Individual Weighted Ergodic Theorem for Bounded Besicovitch Sequences

Published online by Cambridge University Press:  20 November 2018

James H. Olsen
James H. Olsen*
Affiliation:
Department of Mathematical Sciences, North Dakota State University, Fargo North Dakota58105, U.S.A. Mathematics Department, University of Toronto, Toronto, Canada M5S 1A1
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Abstract

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Let (X, , μ) be a σ-finite measure space, p fixed, 1 < p < ∞, T a linear operator of Lp(X,μ), {αi} a sequence of complex numbers. If

exists and is finite a.e. we say the individual weighted ergodic theorem holds for T with the weights {αi}

In this paper we show that if {αi} is a bounded Besicovitch sequence and T is a Dunford-Schwartz operator (i.e.: ||T||1≤1, ||T||∞≤1) then the individual weighted ergodic theorem holds for T with the weights {αi}.

Keywords

47A3528A65
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 4 , 01 December 1982 , pp. 468 - 471
Copyright
Copyright © Canadian Mathematical Society 1982

References

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