Abstract
In extending Bernstein's theorem on the absolute convergence of the Fourier series to Vilenkin groups, Quek and Yap ( J. Math. Anal. Appl. 41 (1980) 1–14) assume that the group G has the boundedness property (P). The main purpose of the present paper is to provide a proof to the result of Quek and Yap without the condition of the boundedness property (P) on G.
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