Multipliers on weighted Hardy spaces over certain totally disconnected groups

Abstract

In this note, we consider the multipliers on weightedH1spaces over totally disconnected locally compact abelian groups with a suitable sequence of open compact subgroups (Vilenkin groups). We first show an(H1,L1)multiplier result from which Onneweer's theorem follows. We also give an(H1,H1)multiplier result under a condition of Baernstein-Sawyer type.