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Weak-type inequalities and convergence of the ergodic averages in variable Lebesgue spaces with weights

Published online by Cambridge University Press:  08 July 2009

M. Isabel Aguilar Cañestro  and
Pedro Ortega Salvador
M. Isabel Aguilar Cañestro
Affiliation:
Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain (mi_aguilar@hotmail.com)
Pedro Ortega Salvador
Affiliation:
Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain (portega@uma.es)
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Abstract

We characterize the weighted weak-type inequalities with variable exponents for the maximal operator associated with an ergodic, invertible, measure-preserving transformation and prove the almost everywhere convergence of the ergodic averages for all functions in a variable Lebesgue space with a weight verifying a suitable condition.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 4 , August 2009 , pp. 673 - 683
Copyright
Copyright © Royal Society of Edinburgh 2009

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