On the modulus of continuity with respect to functions defined on Vilenkin groups
We generalize a theorem of \textit{A. I. Rubinshtejn} [Mat. Zametki 23, 379- 388 (1978; Zbl 0405.43006)]. By the usual definition the modulus of continuity of a function defined on a Vilenkin group, \(G_ m\), can be represented by a sequence of real numbers. Rubinshtejn characterized the sequences which turn to be the modulus of continuity of a function in \(C(G_ m)\), \(L^ 1(G_ m)\), \(L^ 2(G_ m)\). Now we prove his conjecture, namely the theorem is true for \(L^ p(G_ m)\) \((1\leq p<\infty)\) too.
scientific article; zbMATH DE number 3909051
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