Let 0 < α ≤ 1 and let M+α be the Cesàro maximal operator of order α defined by
In this work we characterize the pairs of measurable, positive and locally integrable functions (u, v) for which there exists a constant C > 0 such that the inequality
holds for all λ > 0 and every f in the Orlicz space LΦ(v).
We also characterize the measurable, positive and locally integrable functions w such that the integral inequality
holds for every f ∈ LΦ(w).
The discrete versions of this results allow us, by techniques of transference, to prove weighted inequalities for the Cesàro maximal ergodic operator
associated with an invertible measurable transformation, T, which preserves the measure.Finally, we give sufficient conditions on w for the convergence of the sequence of Cesàro-α ergodic averages for all functions in the weighted Orlicz space LΦ(w).
Weighted inequalities for one-sided maximal functions in Orlicz spaces
