 

Ciprian Demeter and Anthony Quas
WeakL^{1} estimates and ergodic theorems


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


Abstract
We prove that for any dynamical system (X,Σ, m, T), the maximal
operator defined by N*f(x)=sup_{n}(1/n)#{1≦
i:(f(T^{i}x)/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.


Acknowledgements
The second author's research was partially supported by NSF Grant DMS0200703


Author information
Ciprian Demeter:
Department of Mathematics, University of Illinois at Urbana, Urbana, IL 61801
demeter@math.uiuc.edu
Anthony Quas:
Department of Mathematical Sciences, University of Memphis, Memphis, TN 381526429
aquas@memphis.edu

