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oai:riuma.uma.es:10630/313802026-02-03T10:48:48Zcom_10630_2254col_10630_37953

Weighted inequalities for Cesàro maximal operator in Orlicz spaces. Ortega-Salvador, Pedro Ramírez Torreblanca, Consuelo Desigualdades (Matemáticas) Orlicz, Espacios de Análisis matemático 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). 2024-05-24T07:08:02Z 2024-05-24T07:08:02Z 2024-05-24T07:08:02Z 2005-04-26 journal article Salvador PO, Torreblanca CR. Weighted inequalities for Cesàro maximal operators in Orlicz spaces. Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 2005;135(6):1287-1308. doi:10.1017/S0308210500004388 https://hdl.handle.net/10630/31380 10.1017/S0308210500004388 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Cambridge University Press