Oscillation and variation inequalities for convolution powers

Roger L. Jones; Karin Reinhold

doi:10.1017/s0143385701001869

Oscillation and variation inequalities for convolution powers

Roger L. Jones
, Karin Reinhold

Mathematics and Statistics

University at Albany

DePaul University

Research output: Contribution to journal › Article › peer-review

49 Scopus citations

Abstract

We prove L² variation inequalities for operators denned by the convolution powers of probability measures on locally compact Abelian groups. In some cases we also obtain L^p results for 1 < p < ∞. These inequalities imply the pointwise convergence of these operators and give an estimate of the number of upcrossings.

Original language	English
Pages (from-to)	1809-1829
Number of pages	21
Journal	Ergodic Theory and Dynamical Systems
Volume	21
Issue number	6
DOIs	https://doi.org/10.1017/s0143385701001869
State	Published - Dec 2001

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title = "Oscillation and variation inequalities for convolution powers",

abstract = "We prove L2 variation inequalities for operators denned by the convolution powers of probability measures on locally compact Abelian groups. In some cases we also obtain Lp results for 1 < p < ∞. These inequalities imply the pointwise convergence of these operators and give an estimate of the number of upcrossings.",

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AU - Jones, Roger L.

AU - Reinhold, Karin

PY - 2001/12

Y1 - 2001/12

N2 - We prove L2 variation inequalities for operators denned by the convolution powers of probability measures on locally compact Abelian groups. In some cases we also obtain Lp results for 1 < p < ∞. These inequalities imply the pointwise convergence of these operators and give an estimate of the number of upcrossings.

AB - We prove L2 variation inequalities for operators denned by the convolution powers of probability measures on locally compact Abelian groups. In some cases we also obtain Lp results for 1 < p < ∞. These inequalities imply the pointwise convergence of these operators and give an estimate of the number of upcrossings.

UR - https://www.scopus.com/pages/publications/0039567661

U2 - 10.1017/s0143385701001869

DO - 10.1017/s0143385701001869

M3 - Article

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JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 6

ER -

Oscillation and variation inequalities for convolution powers

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