Weighted and vector-valued variational estimates for ergodic averages
  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 H\"older inequality for variation seminorms. 
Ben Krause and Pavel Zorin-Kranich
math.CA math.DS