Weighted integral inequalities for the ergodic maximal operator and other sublinear operators. Convergence of the averages and the ergodic Hilbert transform
Ergodic theorems for certain power bounded operators.
Ergodic results for certain contractions on Orlicz spaces with fixed points.
Orlicz spaces for which the Hardy-Littlewood maximal operators is bounded.
Let M be the Hardy-Littlewood maximal operator defined by: Mf(x) = supx ∈ Q 1/|Q| ∫Q |f| dx, (f ∈ Lloc(Rn)), where the supreme is taken over all cubes Q containing x and |Q| is the Lebesgue measure of Q. In this paper we characterize the Orlicz spaces Lφ*, associated to N-functions φ, such that M is bounded in Lφ*. We prove...
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