[Théorèmes ergodiques ponctuels avec vitesse optimale]
Soit T un opérateur de Dunford–Schwartz sur l'espace de probabilité et . Pour f dans l'image d'opérateurs judicieux de , 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).
Let T be a Dunford–Schwartz operator on the probability space and . For f in the range of suitable operators of , 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).
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@article{CRMATH_2009__347_15-16_953_0,
author = {Cuny, Christophe},
title = {Some optimal pointwise ergodic theorems with rate},
journal = {Comptes Rendus. Math\'ematique},
pages = {953--958},
publisher = {Elsevier},
volume = {347},
number = {15-16},
year = {2009},
doi = {10.1016/j.crma.2009.04.034},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.04.034/}
}
TY - JOUR AU - Cuny, Christophe TI - Some optimal pointwise ergodic theorems with rate JO - Comptes Rendus. Mathématique PY - 2009 SP - 953 EP - 958 VL - 347 IS - 15-16 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.04.034/ DO - 10.1016/j.crma.2009.04.034 LA - en ID - CRMATH_2009__347_15-16_953_0 ER -
%0 Journal Article %A Cuny, Christophe %T Some optimal pointwise ergodic theorems with rate %J Comptes Rendus. Mathématique %D 2009 %P 953-958 %V 347 %N 15-16 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.04.034/ %R 10.1016/j.crma.2009.04.034 %G en %F CRMATH_2009__347_15-16_953_0
Cuny, Christophe. Some optimal pointwise ergodic theorems with rate. Comptes Rendus. Mathématique, Tome 347 (2009) no. 15-16, pp. 953-958. doi : 10.1016/j.crma.2009.04.034. http://www.numdam.org/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.
