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
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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