Boundedness Estimates for Commutators of Riesz Transforms Related to Schrödinger Operators

作     者：Yueshan Wang Yuexiang He 

作者机构：Department of MathematicsJiaozuo UniversityJiaozuo 454003HenanChina 

出 版 物：《Analysis in Theory and Applications》 (分析理论与应用（英文刊）)

年 卷 期：2018年第34卷第4期

页      面：306-322页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Riesz transform Schr?dinger operator commutator Campanato space Hardy space 

摘      要：Let L =-?+V be a Schr?dinger operator on R^n(n ≥ 3), where the non-negative potential V belongs to reverse H?lder class RH_(q1) for q_1n/2. Let H_L^p(R^n)be the Hardy space associated with L. In this paper, we consider the commutator[b,T_α], which associated with the Riesz transform T_α= V~α(-?+V)^(-α) with 0 α ≤ 1,and a locally integrable function b belongs to the new Campanato space Λ_β~θ(ρ). We establish the boundedness of [b,T_α] from L^p(R^n) to L^q(R^n) for 1 p q_1/α with 1/q = 1/p-β/n. We also show that [b,T_α] is bounded from H_L^p(R^n) to L^q(R^n) when n/(n+ β) p ≤ 1,1/q = 1/p-β/n. Moreover, we prove that [b,T_α] maps H_L^(n/n+β)(~Rn)continuously into weak L^1(R^n).