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摘要
Let (X, B, m, tau) be a dynamical system with (X, B, m) a probability space and tau an invertible, measure preserving transformation. This paper deals with the almost everywhere convergence in L-1 (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 {v(i)} defined on Z. We then exhibit cases of such averages where convergence fails.
- 出版日期2012-12
