Weighted Lp spaces and pointwise ergodic theorems.
Sato, Ryotaro
Publicacions Matemàtiques, Tome 39 (1995), p. 273-283 / Harvested from Biblioteca Digital de Matemáticas
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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 averages

R0 n (f,e) = (Σn k=0 Tk f) / (Σn k=0 Tk e)

converge almost everywhere to a function in Lp(W dμ). The characterizations are given for all p, 1 ≤ p < ∞.

Publié le : 1995-01-01
DMLE-ID : 3777 
@article{urn:eudml:doc:41236,
     title = {Weighted Lp spaces and pointwise ergodic theorems.},
     journal = {Publicacions Matem\`atiques},
     volume = {39},
     year = {1995},
     pages = {273-283},
     mrnumber = {MR1370886},
     zbl = {0853.47004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41236}
}

Sato, Ryotaro. Weighted Lp spaces and pointwise ergodic theorems.. Publicacions Matemàtiques, Tome 39 (1995) pp. 273-283. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41236/