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

Canqin Tang

doi:10.1155/2013/865835

Abstract

Lets,τ∈ℝ, q∈(0,∞], andωbe in the classA∞of Muckenhoupt. We introduce the weighted Besov-type spacesB˙p,q,ωs,τ(ℝn)and weighted Triebel-Lizorkin-type spacesF˙p,q,ωs,τ(ℝn)forp∈(0,∞)and then establish theφ-transform characterizations of these new spaces in the sense of Frazier and Jawerth.

Highlights

Function spaces have been a central topic in modern analysis and are of increasing applications in areas such as harmonic analysis and partial differential equations.Since Besov spaces and Triebel-Lizorkin spaces were introduced in [1,2,3], these spaces became the focus of many scholars
We introduce the weighted Besov-type spaces Ḃps,τq,ω(Rn) and weighted Triebel-Lizorkin-type spaces Fṗs,τq,ω(Rn) for p ∈ (0, ∞) and establish the φ-transform characterizations of these new spaces in the sense of Frazier and Jawerth
A series of research results on these topics can be found in [6,7,8,9,10,11,12,13,14,15]. They develop a theory of spaces of Besov-TriebelLizorkin type built on Morrey spaces

Summary

Canqin Tang

Department of Mathematical, Dalian Maritime University, Dalian, Liaoning 116026, China Let s, τ ∈ R, q ∈ (0, ∞], and ω be in the class A∞ of Muckenhoupt. We introduce the weighted Besov-type spaces Ḃps,,τq,ω(Rn) and weighted Triebel-Lizorkin-type spaces Fṗs,,τq,ω(Rn) for p ∈ (0, ∞) and then establish the φ-transform characterizations of these new spaces in the sense of Frazier and Jawerth.

Introduction

Rn dx

Let and