Let 0 < p < ∞, 0 < q ≤ ∞, and s ∈ R. We introduce a new type of generalized Besov-type spaces Bs,φ p,q (Rd) and generalized Triebel–Lizorkin-type spaces Fs,φ p,q (Rd), where φ belongs to the class Gp, that is, φ : (0, ∞) → (0, ∞) is non-decreasing and t−d/pφ(t) is non-increasing in t > 0. These spaces,…