Homogeneous mixed Herz-Morrey spaces and its Applications

Abstract

In this paper, we introduce homogeneous mixed Herz-Morrey spaces $M{\dot{K}}_{p,\vec{q}}^{\alpha ,\lambda }({\mathbb{R}}^n)$ and show it's some properties. Firstly, the boundedness of sublinear operators, fractional type operators in homogeneous mixed Herz-Morrey spaces is investigated. In particular, the above results are still valid for Calder$\acute{o}$n-Zygmund operators and fractional maximal operators. Lastly, the boundedness of their commutators in homogeneous mixed Herz-Morrey spaces is obtained.