Geodesic
Pointwise ergodic theorems for functions in Lorentz spaces $L_{pq}$ with p ≠ ∞
Studia Mathematica, Tome 109 (1994) no. 2, pp. 209-216

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let τ be a null preserving point transformation on a finite measure space. Assuming τ is invertible, P. Ortega Salvador has recently obtained sufficient conditions for the almost everywhere convergence of the ergodic averages in $L_{pq}$ with 1 p ∞, 1 q ∞. In this paper we obtain necessary and sufficient conditions for the almost everywhere convergence, without assuming that τ is invertible and only assuming that p ≠ ∞.
DOI : 10.4064/sm-109-2-209-216
Keywords: pointwise ergodic theorems, $L_{pq}$ spaces, null preserving transformations, measure preserving transformations, positive contractions on $L_1$ spaces

Ryotaro Sato 1

1 
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Ryotaro Sato. Pointwise ergodic theorems for functions in Lorentz spaces $L_{pq}$ with p ≠ ∞. Studia Mathematica, Tome 109 (1994) no. 2, pp. 209-216. doi: 10.4064/sm-109-2-209-216

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