Geodesic
Almost Everywhere Convergence of Convolution Measures
Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 830-841

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Let $\left( X,\,\mathcal{B},\,m,\,\tau\right)$ be a dynamical system with $\left( X,\mathcal{B},m \right)$ a probability space and $\tau $ an invertible, measure preserving transformation. This paper deals with the almost everywhere convergence in ${{\text{L}}^{1}}\left( X \right)$ 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 $\left\{ {{v}_{i}} \right\}$ defined on $\mathbb{Z}$ . We then exhibit cases of such averages where convergence fails.
DOI : 10.4153/CMB-2011-124-3
Mots-clés : 28D 
Reinhold, Karin; Savvopoulou, Anna K.; Wedrychowicz, Christopher M. Almost Everywhere Convergence of Convolution Measures. Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 830-841. doi: 10.4153/CMB-2011-124-3
@article{10_4153_CMB_2011_124_3,
     author = {Reinhold, Karin and Savvopoulou, Anna K. and Wedrychowicz, Christopher M.},
     title = {Almost {Everywhere} {Convergence} of {Convolution} {Measures}},
     journal = {Canadian mathematical bulletin},
     pages = {830--841},
     year = {2012},
     volume = {55},
     number = {4},
     doi = {10.4153/CMB-2011-124-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-124-3/}
}
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AU  - Wedrychowicz, Christopher M.
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ER  - 
%0 Journal Article
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%A Savvopoulou, Anna K.
%A Wedrychowicz, Christopher M.
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%J Canadian mathematical bulletin
%D 2012
%P 830-841
%V 55
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%R 10.4153/CMB-2011-124-3
%F 10_4153_CMB_2011_124_3

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