Almost Everywhere Convergence of Convolution Measures

Canadian mathematical bulletin

Anna K. Savvopoulou¹  Karin Reinhold²  Christopher M. Wedrychowicz¹ 

[1] Department of Mathematical Sciences, Indiana University in South Bend, South Bend, IN, 46545 USA;Department of Mathematics, University at Albany, SUNY, Albany, NY 12222 USA

关键词: non-archimedean Banach spaces;    valued field extensions;    spaces of countable type;    orthogonal bases;   

DOI  :  10.4153/CMB-2011-124-3

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $(X,mathcal{B},m,au)$ be a dynamical system with $(X,mathcal{B},m)$ a probability space and $au$ an invertible, measure preserving transformation. This paper deals with the almost everywhere convergence in $extrm{L}^1(X)$ 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 ${u_i}$ defined on $mathbb{Z}$. We then exhibit cases of such averages where convergence fails.

【 授权许可】

Unknown