On almost everywhere convergence of some sub-sequences of Fejér means for integrable functions on unbounded Vilenkin groups

Memic, Nacima (2014) On almost everywhere convergence of some sub-sequences of Fejér means for integrable functions on unbounded Vilenkin groups. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 30 (1). pp. 91-101. ISSN 0866-0174

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Abstract

By means of G´at’s methods in [2] our aim is to prove the almost everywhere convergence of some sub-sequences of (σnf)n to f, for every integrable function f on unbounded Vilenkin groups. These are in fact sub-sequences of the form (σanMn f)n, where the numbers an are bounded. This result can be considered as a generalization of G´at, s result concerning the almost everywhere convergence of the sequence (σMn f)n on unbounded Vilenkin groups for every integrable function f.

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