Weighted Lp spaces and pointwise ergodic theorems.

Sato, Ryotaro. "Weighted Lp spaces and pointwise ergodic theorems.." Publicacions Matemàtiques 39.2 (1995): 273-283. <http://eudml.org/doc/41236>.

@article{Sato1995,
abstract = {In this paper we give an operator theoretic version of a recent result of F. J. Martín-Reyes and A. de la Torre concerning the problem of finding necessary and sufficient conditions for a nonsingular point transformation to satisfy the Pointwise Ergodic Theorem in Lp. We consider a positive conservative contraction T on L1 of a σ-finite measure space (X, F, μ), a fixed function e in L1 with e &gt; 0 on X, and two positive measurable functions V and W on X. We then characterize the pairs (V,W) such that for any f in Lp(V dμ) the averagesR0n (f,e) = (Σnk=0 Tk f) / (Σnk=0 Tke)converge almost everywhere to a function in Lp(W dμ). The characterizations are given for all p, 1 ≤ p &lt; ∞.},
author = {Sato, Ryotaro},
journal = {Publicacions Matemàtiques},
keywords = {Operadores lineales; Teoría ergódica; nonsingular point transformation; pointwise ergodic theorem; conservative contraction},
language = {eng},
number = {2},
pages = {273-283},
title = {Weighted Lp spaces and pointwise ergodic theorems.},
url = {http://eudml.org/doc/41236},
volume = {39},
year = {1995},
}

TY - JOUR
AU - Sato, Ryotaro
TI - Weighted Lp spaces and pointwise ergodic theorems.
JO - Publicacions Matemàtiques
PY - 1995
VL - 39
IS - 2
SP - 273
EP - 283
AB - In this paper we give an operator theoretic version of a recent result of F. J. Martín-Reyes and A. de la Torre concerning the problem of finding necessary and sufficient conditions for a nonsingular point transformation to satisfy the Pointwise Ergodic Theorem in Lp. We consider a positive conservative contraction T on L1 of a σ-finite measure space (X, F, μ), a fixed function e in L1 with e &gt; 0 on X, and two positive measurable functions V and W on X. We then characterize the pairs (V,W) such that for any f in Lp(V dμ) the averagesR0n (f,e) = (Σnk=0 Tk f) / (Σnk=0 Tke)converge almost everywhere to a function in Lp(W dμ). The characterizations are given for all p, 1 ≤ p &lt; ∞.
LA - eng
KW - Operadores lineales; Teoría ergódica; nonsingular point transformation; pointwise ergodic theorem; conservative contraction
UR - http://eudml.org/doc/41236
ER -