Weak-L1 estimates and ergodic theorems

摘要

We prove that for any dynamical system (X,Σ, m, T), the maximaloperator defined by N*f(x)=supn(1)#{1≦i:(f(Tix)/i)≧ (1)} is almost everywhere finite for fin the Orlicz class Lloglog L(X), extending a result of Assani.As an application, a weighted return times theorem is alsoproved.