Grand variable Herz-Morrey type Besove spaces and Triebel-Lizorkin spaces

In the article, the boundedness of vector-valued sublinear operators in grand variable Herz-Morrey spaces $M{\dot{K}}_{\lambda ,p(\cdot )}^{\eta (\cdot ),q),\theta }\left({\mathbb{R}}^n\right)$ are obtained. Then grand variable Herz-Morrey type Besov and Triebel-Lizorkin spaces are defined. We will also prove the equivalent quasi-norms by Peetre’s maximal operators in these spaces.