The l2-order of magnitude of vilenkin-fourier coefficients

Let G be a compact, metrizable, zero-dimensional, abelian gruop, i.e ., a Vilenkin group. It is well known ([2], [6] for example) that if f belongs to the Lipschitz class Lip (∝, p, G), 0 ≤ ∝ ≤ 1, 1 and lt; p ≤ 2, then its Fourier transform f belongs to ℓB (Ĝ) for p/(p + ∝p - 1) and lt; β ≤ p´ =...