Abstract
AbstractLet (X, ℬ, m, τ) be a dynamical system with (X, ℬ, m) a probability space and τ an invertible, measure preserving transformation. This paper deals with the almost everywhere convergence in L1(X) of a sequence of operators of weighted averages. Almost everywhere convergence follows once we obtain an appropriate maximal estimate and once we provide a dense class where convergence holds almost everywhere. The weights are given by convolution products of members of a sequence of probability measures {vi} defined on ℤ. We then exhibit cases of such averages where convergence fails.
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