Coboundaries of nonconventional ergodic averages

Abstract

Let $(X,\mathcal{A},\mu )$ be a probability measure space and let $T_i,$ $1\le i\le H,$ be invertible bi measurable measure preserving transformations on this measure space. We give a sufficient condition for the product of $H$ bounded functions $f_1,f_2,...,f_H$ to be a coboundary. This condition turns out to be also necessary when one seeks bounded coboundaries.

Results obtained during the 2017 ETDS workshop UNC-CH and presented during the 2018 UNC-CH ETDS workshop

References in corpus (1)

• Pointwise recurrence for commuting measure preserving transformations