Weighted and vector-valued variational estimates for ergodic averages

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.

v2: 12 pages, with a new short proof of the weighted bound for the square function