Hostname: page-component-7479d7b7d-q6k6v Total loading time: 0 Render date: 2024-07-12T15:27:44.526Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)