A note on weighted Besov-type and Triebel-Lizorkin-type spaces

Let s,τ ∈ ℝ,q ∈ (0,∞ ],and ω be in the class a ∞ of muckenhoupt. we introduce the weighted besov-type spaces b ̇ p,q,ω s,τ (ℝ n) and weighted triebel-lizorkin-type spaces f ̇ p,q,ω s,τ (ℝ n) for p ∈ (0,∞) and then establish the φ-transform characterizations of these new spaces in the sense of frazier and jawerth. © 2013 canqin tang.