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Weighted and vector-valued variational estimates for ergodic averages

Published online by Cambridge University Press:  14 July 2016

BEN KRAUSE  and
PAVEL ZORIN-KRANICH Open the ORCID record for PAVEL ZORIN-KRANICH [Opens in a new window]
BEN KRAUSE
Affiliation:
UCLA Math Sciences Building, Los Angeles, CA 90095-1555, USA email [email protected]
PAVEL ZORIN-KRANICH
Affiliation:
Universität Bonn, Mathematisches Institut, Endenicher Allee 60, 53115 Bonn, Germany email [email protected]
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Abstract

We prove weighted and vector-valued variational estimates for ergodic averages on $\mathbb{R}^{d}$. The weighted square function estimate relating ergodic averages to the dyadic martingale is obtained using an $\ell ^{r}$ version of a reverse Hölder inequality for variation seminorms.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 1 , February 2018 , pp. 244 - 256
Copyright
© Cambridge University Press, 2016 

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