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

Abstract: 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.