Atomic decomposition of hardy-morrey spaces with variable exponents

Abstract

The Hardy-Morrey spaces with variable exponents are introduced in terms of maximal functions. The atomic decomposition of Hardy-Morrey spaces with variable exponents is established. This decomposition extends and unifies several atomic decompositions of Hardy type spaces such as the Hardy-Morrey spaces and the Hardy spaces with variable exponents. Some applications of this atomic decomposition on singular integral are presented.