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February, 1976 The Ergodic Maximal Function with Cancellation
Roger L. Jones
Ann. Probab. 4(1): 91-97 (February, 1976). DOI: 10.1214/aop/1176996184

Abstract

A variant of the ergodic maximal function is studied. This maximal function reduces to the usual one for $f \geqq 0$, but the cancellation between the positive and negative parts of $f$ causes interesting behavior. In particular the maximal function can be in $L^1$ even when the function is not in $L \log^+ L$. A relation between this maximal function and the ergodic Hilbert transform is studied.

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Roger L. Jones. "The Ergodic Maximal Function with Cancellation." Ann. Probab. 4 (1) 91 - 97, February, 1976. https://doi.org/10.1214/aop/1176996184

Information

Published: February, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0328.28009
MathSciNet: MR396909
Digital Object Identifier: 10.1214/aop/1176996184

Subjects:
Primary: 28A65
Secondary: 42A36 , 42A40

Keywords: $H^1$ , $L \log^+ L$ , ergodic theory , Flows , Hilbert transform , maximal functions , measure preserving transformations

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 1 • February, 1976
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