CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Almost Everywhere Convergence of Convolution Measures

  Published:2011-06-24
 Printed: Dec 2012
  • Karin Reinhold,
    Department of Mathematics, University at Albany, SUNY, Albany, NY 12222 USA
  • Anna K. Savvopoulou,
    Department of Mathematical Sciences, Indiana University in South Bend, South Bend, IN, 46545 USA
  • Christopher M. Wedrychowicz,
    Department of Mathematical Sciences, Indiana University in South Bend, South Bend, IN, 46545 USA
Format:   LaTeX   MathJax   PDF  

Abstract

Let $(X,\mathcal{B},m,\tau)$ be a dynamical system with $(X,\mathcal{B},m)$ a probability space and $\tau$ an invertible, measure preserving transformation. This paper deals with the almost everywhere convergence in $\textrm{L}^1(X)$ 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 $\{\nu_i\}$ defined on $\mathbb{Z}$. We then exhibit cases of such averages where convergence fails.
MSC Classifications: 28D show english descriptions unknown classification 28D 28D - unknown classification 28D
 

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/