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The limit case of the Cesàro-α convergence of the ergodic averages and the ergodic Hilbert transform

Published online by Cambridge University Press:  11 July 2007

A. L. Bernardis  and
F. J. Martín-Reyes
A. L. Bernardis
Affiliation:
Departamento de Matemáticas, Facultad de Bioquímica y, Ciencias Biológicas, Universidad Nacional del Litoral, 3000 Santa Fe, Argentina ([email protected])
F. J. Martín-Reyes
Affiliation:
Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain ([email protected])
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Abstract

Recently, Sarrión and the authors gave a sufficient condition on invertible Lamperti operators on Lp which guarantees the convergence in the Cesàro-α sense of the ergodic averages and the ergodic Hilbert transform for all f ∈ Lp with p > 1/(1 + α) and −1 < α ≤ 0. The result does not hold for the space L1/(1 + α). In this paper we give a positive result for the smaller Lorentz space L1/(1 + α),1.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 130 , Issue 2 , April 2000 , pp. 225 - 237
Copyright
Copyright © Royal Society of Edinburgh 2000

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