Weak-type inequalities and convergence of the ergodic averages in variable Lebesgue spaces with weights
Published online by Cambridge University Press: 08 July 2009
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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