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December 2020 Modulated ( C , α ) -ergodic theorems with non-integral orders for Dunford–Schwartz operators
Takeshi Yoshimoto
Illinois J. Math. 64(4): 613-644 (December 2020). DOI: 10.1215/00192082-8746145

Abstract

The definition of the usual p th Weyl semi-norm for sequences is extended to the case of ( C , α ) averages for 0 < α 1 and the ( p , α ) -Besicovitch sequences are defined similarly to the classical case α = 1 . We study the effects of ( p , α ) -Besicovitch sequences with non-integral orders as good modulators. The major finding is the almost everywhere convergence of ( C , α ) ergodic averages with discrete and continuous ( p , α ) -Besicovitch modulators for Dunford–Schwartz operators. The results have the additional advantage that they are sufficiently general to give as corollaries a (new) weighted Abelian ergodic theorem and the a.e. convergence of random ( C , α ) -ergodic averages for Dunford–Schwartz operators.

Citation

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Takeshi Yoshimoto. "Modulated ( C , α ) -ergodic theorems with non-integral orders for Dunford–Schwartz operators." Illinois J. Math. 64 (4) 613 - 644, December 2020. https://doi.org/10.1215/00192082-8746145

Information

Received: 30 March 2020; Revised: 15 July 2020; Published: December 2020
First available in Project Euclid: 28 September 2020

zbMATH: 07269223
MathSciNet: MR4164449
Digital Object Identifier: 10.1215/00192082-8746145

Subjects:
Primary: 40H05
Secondary: 47A35

Rights: Copyright © 2020 University of Illinois at Urbana-Champaign

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Vol.64 • No. 4 • December 2020
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