# Weighted Lp spaces and pointwise ergodic theorems.

Publicacions Matemàtiques (1995)

- Volume: 39, Issue: 2, page 273-283
- ISSN: 0214-1493

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topSato, 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 > 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 < ∞.},

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 > 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 < ∞.

LA - eng

KW - Operadores lineales; Teoría ergódica; nonsingular point transformation; pointwise ergodic theorem; conservative contraction

UR - http://eudml.org/doc/41236

ER -

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