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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-KRANICHOpen 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 benkrause23@math.ucla.edu
PAVEL ZORIN-KRANICH
Affiliation:
Universität Bonn, Mathematisches Institut, Endenicher Allee 60, 53115 Bonn, Germany email pzorin@uni-bonn.de
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Abstract

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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.

Information

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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