A Local Ergodic Theorem on Lp
Canadian journal of mathematics, Tome 26 (1974) no. 5, pp. 1206-1216
Voir la notice de l'article provenant de la source Cambridge University Press
Two general types of pointwise ergodic theorems have been studied: those as t approaches infinity, and those as t approaches zero. This paper deals with the latter case, which is referred to as the local case.Let (X, , μ) be a complete, σ-finite measure space. Let {Tt } be a strongly continuous one-parameter semi-group of contractions on , defined for t ≧ 0. For Tt positive, it was shown independently in [2] and [5] that 1.1 almost everywhere on X, for any f ∊ L1. The same result was obtained in [1], with the continuity assumption weakened to having it hold for t > 0.
Baxter, J. R.; Chacon, R. V. A Local Ergodic Theorem on Lp. Canadian journal of mathematics, Tome 26 (1974) no. 5, pp. 1206-1216. doi: 10.4153/CJM-1974-114-8
@article{10_4153_CJM_1974_114_8,
author = {Baxter, J. R. and Chacon, R. V.},
title = {A {Local} {Ergodic} {Theorem} on {Lp}},
journal = {Canadian journal of mathematics},
pages = {1206--1216},
year = {1974},
volume = {26},
number = {5},
doi = {10.4153/CJM-1974-114-8},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-114-8/}
}
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