Geodesic
Multiparameter Weighted Ergodic Theorems
Canadian journal of mathematics, Tome 46 (1994) no. 2, pp. 343-356

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we show that multi-dimensional bounded Besicovitch weights are good weights for the pointwise ergodic theorem for Dunford-Schwartz operators and positively dominated contractions of LP . This in particular implies new weighted results for multi-parameter measure preserving point transformations. The proofs show that Besicovitch weights are a very natural class when considered from the operator point of view. We also show that for 1 ≤ r < ∞, the r-bounded Besicovitch classes are all the same, generalizing a result of Bellow and Losert. 
Jones, Roger L.; Olsen, James. Multiparameter Weighted Ergodic Theorems. Canadian journal of mathematics, Tome 46 (1994) no. 2, pp. 343-356. doi: 10.4153/CJM-1994-017-8
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