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Oscillation and variation inequalities for convolution powers

Published online by Cambridge University Press:  28 November 2001

ROGER L. JONES  and
KARIN REINHOLD
ROGER L. JONES
Affiliation:
Department of Mathematics, DePaul University, 2320 N. Kenmore, Chicago IL60614, USA
KARIN REINHOLD
Affiliation:
Department of Mathematics, University at Albany, SUNY, 1400 Washington Ave., Albany, NY 12222, USA (e-mail: reinhold@math.albany.edu)
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Abstract

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We prove L^2 variation inequalities for operators defined by the convolution powers of probability measures on locally compact Abelian groups. In some cases we also obtain L^p results for 1<p<\infty. These inequalities imply the pointwise convergence of these operators and give an estimate of the number of upcrossings.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 6 , December 2001 , pp. 1809 - 1829
Copyright
2001 Cambridge University Press