Transference of weak type bounds of multiparameter ergodic and geometric maximal operators

Abstract

Let $U_{1}, \ldots, U_{d}$ be a non-periodic collection of commuting measure preserving transformations on a probability space $(\Omega, \Sigma, \mu).$ Also let $\Gamma$ be a nonempty subset of $\mathbb{Z}^{d}_{+}$ and $\mathcal B$ the associated collect