Convergence of the averages and finiteness of ergodic power funtions in weighted L1 spaces.

Ortega Salvador, Pedro. "Convergence of the averages and finiteness of ergodic power funtions in weighted L1 spaces.." Publicacions Matemàtiques 35.2 (1991): 465-473. <http://eudml.org/doc/41703>.

@article{OrtegaSalvador1991,
abstract = {Let (X, F, μ) be a finite measure space. Let T: X → X be a measure preserving transformation and let Anf denote the average of Tkf, k = 0, ..., n. Given a real positive function v on X, we prove that \{Anf\} converges in the a.e. sense for every f in L1(v dμ) if and only if infi ≥ 0 v(Tix) &gt; 0 a.e., and the same condition is equivalent to the finiteness of a related ergodic power function Prf for every f in L1(v dμ). We apply this result to characterize, being T null-preserving, the finite measures ν for which the sequence \{Anf\} converges a.e. for every f ∈ L1(dν) and to prove that uniform boundedness of the averages in L1 is sufficient for finiteness a.e. of Pr.},
author = {Ortega Salvador, Pedro},
journal = {Publicacions Matemàtiques},
keywords = {maximal operator; convergence; weighted spaces; measure- preserving transformation; finiteness; ergodic power function; averages},
language = {eng},
number = {2},
pages = {465-473},
title = {Convergence of the averages and finiteness of ergodic power funtions in weighted L1 spaces.},
url = {http://eudml.org/doc/41703},
volume = {35},
year = {1991},
}

TY - JOUR
AU - Ortega Salvador, Pedro
TI - Convergence of the averages and finiteness of ergodic power funtions in weighted L1 spaces.
JO - Publicacions Matemàtiques
PY - 1991
VL - 35
IS - 2
SP - 465
EP - 473
AB - Let (X, F, μ) be a finite measure space. Let T: X → X be a measure preserving transformation and let Anf denote the average of Tkf, k = 0, ..., n. Given a real positive function v on X, we prove that {Anf} converges in the a.e. sense for every f in L1(v dμ) if and only if infi ≥ 0 v(Tix) &gt; 0 a.e., and the same condition is equivalent to the finiteness of a related ergodic power function Prf for every f in L1(v dμ). We apply this result to characterize, being T null-preserving, the finite measures ν for which the sequence {Anf} converges a.e. for every f ∈ L1(dν) and to prove that uniform boundedness of the averages in L1 is sufficient for finiteness a.e. of Pr.
LA - eng
KW - maximal operator; convergence; weighted spaces; measure- preserving transformation; finiteness; ergodic power function; averages
UR - http://eudml.org/doc/41703
ER -