Embedding theorem on spaces of homogeneous type

In [5] the embedding theorem for the Besov spaces Ḃ_p^α,q with -ε < α < ε and 1 ≤ p, q ≤ ∞, and Triebel-Lizorkin spaces Ḟ_p^α,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 Ḃ_p^α,q with p₀ < p ≤ ∞ and 0 < q ≤ ∞ for p₀ < 1, and the Triebel-Lizorkin spaces Ḟ_p^α,q with p₁ < p < ∞ and p₁ < q < ∞ for p₁ < 1. The proofs are new even for ℝⁿ.