Geodesic
$\Lambda$-summability and multiplicators of H\"older classes of Fourier series with respect to character systems
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 2, pp. 3-8

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Let $G$ be a Vilenkin group of bounded type. We obtain nessesary and sufficient conditions of uniform $\Lambda$-summability for all Fourier series of $f\in C(G)$ and one of $\Lambda$-summability in $L^1(G)$ for all Fourier series of $f\in L^1(G)$. Also we extend some T. Quek and L. Yap results to the case of general modulus of continuity. 
@article{ISU_2011_11_2_a0,
     author = {N. Yu. Agafonova},
     title = {$\Lambda$-summability and multiplicators of {H\"older} classes of {Fourier} series with respect to character systems},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {3--8},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2011_11_2_a0/}
}
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N. Yu. Agafonova. $\Lambda$-summability and multiplicators of H\"older classes of Fourier series with respect to character systems. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 2, pp. 3-8. http://geodesic.mathdoc.fr/item/ISU_2011_11_2_a0/