Differential and ergodic transforms
type: Item
instance of: scholarly article
title: Differential and ergodic transforms
zbMATH Open document ID: 1005.28012
author: Roger Jones
author: J. Rosenblatt
published in: Mathematische Annalen
publication date: 2002-09-17T00:00:00Z
review text: Let \(\tau\) be an ergodic transformation with respect to a non-atomic measure. Operators of the form \[ T_nf(x)=\sum_{k=1}^nv_k\left((1/n_k)\sum_{j=0}^{n_k-1}f(\tau^jx)- (1/n_{k-1})\sum_{j=0}^{n_{k-1}-1}f(\tau^jx)\right) \] for a lacunary sequence \((n_k)\) and \(\ell^{\infty}\) sequence of weights \((v_k)\) are shown to converge a.e. and in \(L^p\), \(1<p<\infty\). Related results on dyadic differentiation and the dyadic martingale are found.
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 42C20
Mathematics Subject Classification ID: 60G46
Mathematics Subject Classification ID: 37A05
zbMATH DE Number: 1801614
zbMATH Keywords: ergodic averages
zbMATH Keywords: differential transform
zbMATH Keywords: dyadic differentiation
zbMATH Keywords: dyadic martingale
reviewed by: Thomas B. Ward
MaRDI profile type: Publication
full work available at URL: s002080200313
OpenAlex ID: W2049420934
DOI: 10.1007/S002080200313
description: scientific article; zbMATH DE number 1801614