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Differential and ergodic transforms

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Abstract.

In this paper we consider weighted differences of ergodic averages and averages associated with differentiation. These weighted differences are shown to converge a.e., as well as in \(L^p, 1<p<\infty\). These results have consequences for unconditional convergence of the series of differences, and give some information about how the averages converge.

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Authors and Affiliations

  1. DePaul University, Department of Mathematics, 2330 N. Kenmore, Chicago, IL 60614, USA (e-mail: rjones@condor.depaul.edu) , , , , , , US

    Roger L. Jones

  2. University of Illinois at Urbana, Department of Mathematics, Urbana, IL 61801, USA (e-mail: rosnbltt@math.uiuc.edu) , , , , , , US

    Joseph Rosenblatt

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  1. Roger L. Jones
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  2. Joseph Rosenblatt
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Received: 6 March 2000 / Published online: 4 April 2002

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Jones, R., Rosenblatt, J. Differential and ergodic transforms. Math Ann 323, 525–546 (2002). https://doi.org/10.1007/s002080200313

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  • DOI: https://doi.org/10.1007/s002080200313

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