Moving Weighted Averages

Akcoglu, M. A. ; Déniel, Y.

Canadian journal of mathematics, Tome 45 (1993) no. 3, pp. 449-469

Résumé

Let R denote the real line. Let {Tt }tєR be a measure preserving ergodic flow on a non atomic finite measure space (X, F, μ). A nonnegative function φ on R is called a weight function if ∫R φ(t)dt = 1. Consider the weighted ergodic averages of a function f X —> R, where {θk} is a sequence of weight functions. Some sufficient and some necessary and sufficient conditions are given for the a.e. convergence of Akf, in particular for a special case in which where φ is a fixed weight function and {(ak, rk )} is a sequence of pairs of real numbers such that rk > 0 for all k. These conditions are obtained by a combination of the methods of Bellow-Jones-Rosenblatt, developed to deal with moving ergodic averages, and the methods of Broise-Déniel-Derriennic, developed to deal with unbounded weight functions.

Détail

DOI : 10.4153/CJM-1993-023-x

Mots-clés : 28D99, 47A35, maximal ergodic theorems, rearrangements

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