Calderón-Zygmund operators on weighted weak hardy spaces in locally compact Vilenkin groups

Abstract

Let G be a bounded locally compact Vilenkin group. We study the atomic decomposition of weighted weak Hardy space. We also define several Calderón-Zygmund type operators and study their boundedness on spaces like weighted Hardy spaces, weighted weak Hardy spaces and weighted weak Lebesgue spaces. Sharpness of some of our results is also discussed.