In  the embedding theorem for the Besov spaces Ḃpα,q with -ε < α < ε and 1 ≤ p, q ≤ ∞, and Triebel-Lizorkin spaces Ḟpα,q with -ε < α < ε and 1 < p, q < ∞, on spaces of homogeneous type was obtained. In this article the embedding theorem is generalized to the Besov spaces Ḃpα,q with p0 < p ≤ ∞ and 0 < q ≤ ∞ for p0 < 1, and the Triebel-Lizorkin spaces Ḟpα,q with p1 < p < ∞ and p1 < q < ∞ for p1 < 1. The proofs are new even for ℝn.
- Besov and Triebel-Lizorkin spaces
- Discrete Calderón formula
- Embedding theorem
- Spaces of homogeneous type