Intrinsic atomic and molecular decompositions of Hardy–Musielak–Orlicz spaces

Abstract

We introduce the Hardy type space for Musielak–Orlicz spaces. It includes several existing Hardy type spaces such as the Hardy–Orlicz spaces and the Hardy spaces with variable exponents. Furthermore, we develop an atomic decomposition such that the size condition just relies on the norms of Musielak–Orlicz spaces. This gives us a nature extension of the molecular decompositions to the Hardy type space for Musielak–Orlicz spaces.