Almost everywhere convergence and boundedness of Cesaro-alpha ergodic averages

Authors
Martin-Reyes, FJ Gavilan, MDS
Citation
Fj. Martin-reyes et Mds. Gavilan, Almost everywhere convergence and boundedness of Cesaro-alpha ergodic averages, ILL J MATH, 43(3), 1999, pp. 592-611
Citations number
24
Categorie Soggetti
Mathematics
Journal title
ILLINOIS JOURNAL OF MATHEMATICS
ISSN journal
00192082 → ACNP
Volume
43
Issue
3
Year of publication
1999
Pages
592 - 611
Database
ISI
SICI code
0019-2082(199923)43:3<592:AECABO>2.0.ZU;2-Y
Abstract
We study the almost everywhere convergence of the ergodic Cesaro-alpha aver ages R-n,R-alpha f = 1/A(n)(alpha) Sigma(i=0)(n) A(n-1)(alpha-1) T(1)f and the boundedness of the ergodic maximal operator M(alpha)f = sup(n is an ele ment of N) [R(n,alpha)f], associated with a positive linear operator T with positive inverse on some L-p(mu), 1 < p < infinity, 0 < alpha less than or equal to 1.