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Ciprian Demeter and Anthony Quas
Weak-L1 estimates and ergodic theorems
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| Published: |
June 15, 2004 |
| Keywords: |
Return times theorem, Orlicz spaces |
| Subject: |
37A30, 46E30, 60F15 |
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Abstract
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.
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| Acknowledgements
The second author's research was partially supported by NSF Grant DMS-0200703
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| 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 38152-6429
aquas@memphis.edu
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