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.

Boundedness of Hardy-Littlewood maximal operator on block spaces with variable exponent

“…We have the following proposition from [12]. For completeness, we provide the proof of the subsequent result from [12]. Proposition 3.2.…”

“…For the boundedness of the Hardy-Littlewood maximal operator on a Morrey space with variable exponents, the reader is referred to [11]. In addition, the extension of the boundedness of the maximal operator on a vector-valued Morrey space with variable exponents is obtained in [17], [12]. Proposition 3.1.…”

Intrinsic Square Functions on Morrey and Block Spaces with Variable Exponents

“…On the other hand, there are several versions of Morrey spaces with variable exponents, see [1,13,15,20,24]. Therefore, we begin with the definition of the family of Morrey spaces with variable exponents used in this paper.…”

Some norm inequalities in Musielak-Orlicz spaces

“…Using the vector-valued inequality, in Section 7 we shall establish a decomposition result for functions in Musielak-Orlicz spaces as an extension of [23] and [24] for the case of Lebesgue spaces with variable exponents and Orlicz spaces. See [4,13,14,26,27,37] for related results. As an application of the decomposition result, we obtain an Olsen inequality in the final section.…”