Geodesic
Divergent square averages
Zoltán Buczolich 1 ; R. Daniel Mauldin2
1 Department of Analysis, Eötvös Loránd<br/>University, Pázmány Péter Sétány 1/c, 1117 Budapest, Hungary
2 University of North Texas<br/>Department of Mathematics<br/>Denton 76203-1430<br/>United States
Annals of mathematics, Tome 171 (2010) no. 3, pp. 1479-1530.

Voir la notice de l'article provenant de la source Annals of Mathematics website

In this paper we answer a question of J. Bourgain which was motivated by questions A. Bellow and H. Furstenberg. We show that the sequence $\{ n^{2}\}_{n=1}^{\infty}$ is $L^{1}$-universally bad. This implies that it is not true that given a dynamical system $(X ,\Sigma, \mu, T)$ and $f\in L^{1}(\mu)$, the ergodic means \[ \lim_{N\to \infty}\frac{1}N\sum _{n=1}^{N}f(T^{n^{2}}(x)) \] converge almost surely.
DOI : 10.4007/annals.2010.171.1479

Zoltán Buczolich  1 ; R. Daniel Mauldin 2

1 Department of Analysis, Eötvös Loránd<br/>University, Pázmány Péter Sétány 1/c, 1117 Budapest, Hungary
2 University of North Texas<br/>Department of Mathematics<br/>Denton 76203-1430<br/>United States 
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Zoltán Buczolich ; R. Daniel Mauldin. Divergent square averages. Annals of mathematics, Tome 171 (2010) no. 3, pp. 1479-1530. doi : 10.4007/annals.2010.171.1479. http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.171.1479/

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