Geodesic
Multi-parameter setting (c, α) means with respect to one dimensional Vilenkin system
Filomat, Tome 35 (2021) no. 12, p. 4121

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DOI

We prove that the maximal operator of the (C, α n)-means of the one dimensional Vilenkin-Fourier series is of weak type(L 1 , L 1). Moreover, we prove the almost everywhere convergence of the (C, α n) means of integrable functions (i.e. σ αn n f −→ f), where n ∈ N α, q and n −→ ∞ for f ∈ L 1 (G m), G m is a bounded Vilenkin group, for every sequence α = (α n), 0 α n 1
DOI : 10.2298/FIL2112121G
Classification : 42C10
Keywords: One dimensional Vilenkin System, Vilenkin-Fourier series, almost everywhere convergence, (C, αn) means 
György Gát; Anteneh Tilahun. Multi-parameter setting (c, α) means with respect to one dimensional Vilenkin system. Filomat, Tome 35 (2021) no. 12, p. 4121 . doi: 10.2298/FIL2112121G
@article{10_2298_FIL2112121G,
     author = {Gy\"orgy G\'at and Anteneh Tilahun},
     title = {Multi-parameter setting (c, \ensuremath{\alpha}) means with respect to one dimensional {Vilenkin} system},
     journal = {Filomat},
     pages = {4121 },
     year = {2021},
     volume = {35},
     number = {12},
     doi = {10.2298/FIL2112121G},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2112121G/}
}
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