Abstract.
Let G be a compact, metrizable, zero - dimensional, abelian group, i.e., a Vilenkin group. It is well known ( [2], [6] for example ) that if f belongs to the Lipschitz class Lip ( \alpha, p, G ), 0 ( p - 1 ), where \widehat G is the dual of G. For Lipschitz functions on the real line R and on the circle group T ( [3], Theorem 85, p. 117; [5], Theorem ( 1.3 )c, p. 108 ), the special case p = 2, 0 < \alpha < 1, reveals some reversibility between the conditions on f and \widehat f. In the present work we extend, among other things, this reversibility to the L2 - Lipschitz functions on Vilenkin groups.
