Littlewood-Paley and multiplier theorems on weighted spaces over locally compact Vilenkin groups

Abstract

We extend the Littlewood-Paley theorem to Lp w(G), where G is a locally compact Vilenkin group and w are weights satisfying the Muckenhoupt Ap condition. As an application we obtain a mixed-norm type multiplier result on Lp w(G) and prove the sharpness of our result. We also obtain a sufficient condition for φ ∈ L∞(Γ) to be a multiplier on the power weighted Lp α(G) in terms of its smoothness condition. © 1997 Academic Press.