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Multiparameter Weighted Ergodic Theorems

Published online by Cambridge University Press:  20 November 2018

Roger L. Jones  and
James Olsen
Roger L. Jones
Affiliation:
Department of Mathematics DePaul University 2219N.Kenmore Chicago, Illinois 60614 U.S.A. e-mail:MATRUJ@DePaul.Bitnet
James Olsen
Affiliation:
Department of Mathematics North Dakota State University Fargo, North Dakota 58105 U.S.A. e-mail:JOlsen@Plains.NoDak.edu
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Abstract

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In this paper we show that multi-dimensional bounded Besicovitch weights are good weights for the pointwise ergodic theorem for Dunford-Schwartz operators and positively dominated contractions of LP. This in particular implies new weighted results for multi-parameter measure preserving point transformations. The proofs show that Besicovitch weights are a very natural class when considered from the operator point of view. We also show that for 1 ≤ r < ∞, the r-bounded Besicovitch classes are all the same, generalizing a result of Bellow and Losert.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 2 , 01 April 1994 , pp. 343 - 356
Copyright
Copyright © Canadian Mathematical Society 1994

References

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