Hostname: page-component-7bb8b95d7b-w7rtg Total loading time: 0 Render date: 2024-09-20T16:26:18.561Z Has data issue: false hasContentIssue false
  • English
  • Français

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 (bernard@alpha.arcride.edu.ar)
F. J. Martín-Reyes
Affiliation:
Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain (martin@anamat.cie.uma.es)
Get access Rights & Permissions [Opens in a new window]

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

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.)