On the modulus of continuity with respect to functions defined on Vilenkin groups

Abstract

ha this paper we generalize a theorem of Rubinstein [2]. By the usual definition the modulus of continuity of a function defined on a Vilm,&in group (G,,) can be represented by a sequence of real numbers. Rubinstein [2] characterized the sequences which turn to be the modulus of continuity of a function in C(G,,), L~(G~), LZ(G=). Now we prove his conjecture, namely the theorem is true for LP(Gm) (t ~ p < ~) too.