Pointwise ergodic theorems in Lorentz spaces L(p,q) for null preserving transformations
Studia Mathematica, Tome 114 (1995) no. 3, pp. 227-236
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Let (X,ℱ,µ) be a finite measure space and τ a null preserving transformation on (X,ℱ,µ). Functions in Lorentz spaces L(p,q) associated with the measure μ are considered for pointwise ergodic theorems. Necessary and sufficient conditions are given in order that for any f in L(p,q) the ergodic average $n^{-1} ∑^{n-1}_{i=0} f∘τ^{i}(x)$ converges almost everywhere to a function f* in $L(p_1,q_1]$, where (pq) and $(p_1,q_1]$ are assumed to be in the set ${(r,s) : r=s=1, or 1 r ∞ and 1 ≤ s ≤ ∞, or r = s = ∞}$. Results due to C. Ryll-Nardzewski, S. Gładysz, and I. Assani and J. Woś are generalized and unified
@article{10_4064_sm_114_3_227_236,
author = {Ryotaro Sato},
title = {Pointwise ergodic theorems in {Lorentz} spaces {L(p,q)} for null preserving transformations},
journal = {Studia Mathematica},
pages = {227--236},
publisher = {mathdoc},
volume = {114},
number = {3},
year = {1995},
doi = {10.4064/sm-114-3-227-236},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-114-3-227-236/}
}
TY - JOUR AU - Ryotaro Sato TI - Pointwise ergodic theorems in Lorentz spaces L(p,q) for null preserving transformations JO - Studia Mathematica PY - 1995 SP - 227 EP - 236 VL - 114 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-114-3-227-236/ DO - 10.4064/sm-114-3-227-236 LA - en ID - 10_4064_sm_114_3_227_236 ER -
%0 Journal Article %A Ryotaro Sato %T Pointwise ergodic theorems in Lorentz spaces L(p,q) for null preserving transformations %J Studia Mathematica %D 1995 %P 227-236 %V 114 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm-114-3-227-236/ %R 10.4064/sm-114-3-227-236 %G en %F 10_4064_sm_114_3_227_236
Ryotaro Sato. Pointwise ergodic theorems in Lorentz spaces L(p,q) for null preserving transformations. Studia Mathematica, Tome 114 (1995) no. 3, pp. 227-236. doi: 10.4064/sm-114-3-227-236
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