Herz--Morrey type Besov and Triebel-Lizorkin spaces with variable exponents

Abstract

In the article, the boundedness of vector-valued sublinear operators in Herz--Morrey spaces with variable exponents $M\dot{K}^{\alpha(\cdot),\lambda}_{q,p(\cdot)}(\mathbb{R}^{n})$ are obtained. Then Herz--Morrey type Besov and Triebel-Lizorkin spaces with variable exponents are introduced. Finally, we prove the equivalent quasi-norms on these spaces by Peetre's maximal operators.