A+ CATEGORY SCIENTIFIC UNIT

Pointwise ergodic theorems for functions in Lorentz spaces $L_{pq}$ with p ≠ ∞

Volume 109 / 1994

Ryotaro Sato Studia Mathematica 109 (1994), 209-216 DOI: 10.4064/sm-109-2-209-216

Abstract

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 ≠ ∞.

Authors

  • Ryotaro Sato

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image