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Oscillation and variation for the Gaussian Riesz transforms and Poisson integral

Published online by Cambridge University Press:  12 July 2007

E. Harboure ,
R. A. Macías ,
M. T. Menárguez  and
J. L. Torrea
E. Harboure
Affiliation:
Departamento de Matemática, Facultad de Ingenierí a Química, Universidad Nacional del Litoral, (3000) Santa Fe y CONICET, Argentina (harbour@ceride.gov.ar)
R. A. Macías
Affiliation:
Departamento de Matemática, Facultad de Ingenierí a Química, Universidad Nacional del Litoral, (3000) Santa Fe y CONICET, Argentina (rmacias@ceride.gov.ar)
M. T. Menárguez
Affiliation:
ETS I de Caminos, Canales y Puertos, Universidad Politécnica de Madrid, Ciudad Universitaria s/n, 28040 Madrid, Spain (tmenar@dumbo.caminos.upm.es)
J. L. Torrea
Affiliation:
Facultad de Ciencias, Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, 28049 Madrid, Spain (joseluis.torrea@uam.es)
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Abstract

For the family of truncations of the Gaussian Riesz transforms and Poisson integral we study their rate of convergence through the oscillation and variation operators. More precisely, we search for their Lp (dγ)-boundedness properties, where dγ denotes the Gauss measure. We achieve our results by looking at the oscillation and variation operators from a vector-valued point of view.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 135 , Issue 1 , February 2005 , pp. 85 - 104
Copyright
Copyright © Royal Society of Edinburgh 2005

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