Generalized Besov-type and Triebel--Lizorkin-type spaces

Let $0 \lt p \lt \infty $, $0 \lt q\leq \infty $, and $s\in \mathbb R$. We introduce a new type of generalized Besov-type spaces $B_{p,q}^{s,\varphi }(\mathbb {R}^d)$ and generalized Triebel--Lizorkin-type spaces $F_{p,q}^{s,\varphi }(\mathbb {R}^d)$, whe