Almost everywhere convergence and boundedness of Cesàro-[alpha] ergodic averages in Lp,q-spaces

Abstract

Let (X,µ) be a [sigma]-finite measure space and let [tau] be an ergodic invertible measure preserving transformation. We study the a.e. convergence of the Cesàro-[alpha] ergodic averages associated with [tau] and the boundedness of the corresponding maximal operator in the setting of Lp,q(wdµ) spaces.