Comptes Rendus
Dynamical Systems/Probability Theory
Some optimal pointwise ergodic theorems with rate
Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 953-958.

Let T be a Dunford–Schwartz operator on the probability space (X,Σ,μ) and p>1. For f in the range of suitable operators of Lp(X,Σ,μ), we obtain pointwise ergodic theorems with rate, using a method of Derriennic and Lin (2001). When T is induced by a μ-preserving transformation, these results are shown to be optimal. The proof of the optimality is inspired from a construction of Déniel (1989).

Soit T un opérateur de Dunford–Schwartz sur l'espace de probabilité (X,Σ,μ) et p>1. Pour f dans l'image d'opérateurs judicieux de Lp(X,Σ,μ), nous obtenons des théorèmes ergodiques ponctuels avec vitesse, par une méthode due à Derriennic et Lin (2001). Lorsque T est induit par une transformation préservant μ, nous montrons l'optimalité des résultats, la preuve étant inspirée par une construction de Déniel (1989).

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.04.034

Christophe Cuny 1

1 Université de la Nouvelle-Calédonie, Équipe ERIM, B.P. R4, 98800 Nouméa, New Caledonia
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Christophe Cuny. Some optimal pointwise ergodic theorems with rate. Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 953-958. doi : 10.1016/j.crma.2009.04.034. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.04.034/

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Research partially carried out at Ben-Gurion University, supported by its Center for Advanced Studies in Mathematics.

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