New York Journal of Mathematics
Volume 10 (2004) 169-174


Ciprian Demeter and Anthony Quas

Weak-L1 estimates and ergodic theorems

Published: June 15, 2004
Keywords: Return times theorem, Orlicz spaces
Subject: 37A30, 46E30, 60F15

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


The second author's research was partially supported by NSF Grant DMS-0200703

Author information

Ciprian Demeter:
Department of Mathematics, University of Illinois at Urbana, Urbana, IL 61801

Anthony Quas:
Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152-6429