A Note on Weighted Besov-Type and Triebel-Lizorkin-Type Spaces

Abstract EN

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,ωs,τ(ℝn) and weighted Triebel-Lizorkin-type spaces F˙p,q,ωs,τ(ℝn) for p∈(0,∞) and then establish the φ-transform characterizations of these new spaces in the sense of Frazier and Jawerth.