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- W3089515886 abstract "The definition of the usual p th Weyl semi-norm for sequences is extended to the case of ( C , α ) averages for 0 < α ≤ 1 and the ( p , α ) -Besicovitch sequences are defined similarly to the classical case α = 1 . We study the effects of ( p , α ) -Besicovitch sequences with non-integral orders as good modulators. The major finding is the almost everywhere convergence of ( C , α ) ergodic averages with discrete and continuous ( p , α ) -Besicovitch modulators for Dunford–Schwartz operators. The results have the additional advantage that they are sufficiently general to give as corollaries a (new) weighted Abelian ergodic theorem and the a.e. convergence of random ( C , α ) -ergodic averages for Dunford–Schwartz operators." @default.
- W3089515886 created "2020-10-08" @default.
- W3089515886 creator A5035748601 @default.
- W3089515886 date "2020-12-01" @default.
- W3089515886 modified "2023-09-23" @default.
- W3089515886 title "Modulated ( C , α ) -ergodic theorems with non-integral orders for Dunford–Schwartz operators" @default.
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- W3089515886 doi "https://doi.org/10.1215/00192082-8746145" @default.
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