an:00149656
Zbl 0774.41026
Tateoka, J.
The modulus of continuity and the best approximation over the dyadic group
EN
Acta Math. Hung. 59, No. 1-2, 115-120 (1992).
00008456
1992
j
41A50 41A17 41A27 46A16
The connection between the modulus of continuity and the best approximation of functions by Walsh polynomials was studied by \textit{C. Watari} [Tohoku Math. J., II. Ser. 15, 1-5 (1963; Zbl 0111.265)] for \(L^ p\) space, \(1\leq p<\infty\). A similar result for \(0<p<1\) was obtained by \textit{E. A. Storozenko}, \textit{V. G. Krotov} and \textit{P. Oswal'd} [Math. Sb., n. Ser. 98(140), 395-415 (1975; Zbl 0314.41004)]. On the other hand, direct and converse theorems for the Hardy space \(H^ p\), \(0<p<\infty\), over the \(n\)-dimensional torus were proved by \textit{L. Colzani} [Ann. Math. Pure Appl., IV. Ser. 137, 207-215 (1984; Zbl 0558.41017)]. In this paper these results for the \(H^ p\) space, \(0<p\leq 1\) and VMO space over the dyadic group are proved.
D.Zarnadze (Tbilisi)
Zbl 0314.41004; Zbl 0558.41017; Zbl 0111.265