Herz-type Hardy spaces on Vilenkin groups and their applications

Abstract

Let 1 q q ≦ α p G be a locally compact Vilenkin group. The authors first introduce the general Herz-type Hardy spaces H K q α,p (G) and h K q α,p (G) , then present the central atom or the central block and atom decompositions of these spaces. Using this characterization, they discuss some properties of these spaces and investigate the boundedness on the spaces H K q α,p (G) of the fractional integral operators and the boundedness on the spaces h K q α,p (G) of the pseudo-differential operators of order zero.