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).
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).
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Christophe Cuny 1
@article{CRMATH_2009__347_15-16_953_0, author = {Christophe Cuny}, 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}, }
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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