中文摘要：

令L=-△＋V是薛定谔算子,其中△是R^n上的拉普拉斯算子,并且非负位势V属于逆H？lder类Bq（q≥n/2）.与算子L相关的Riesz变换记为T1=V（-△＋V）^（-1）和T2=V^（-1/2）（-△＋V）^（-1/2）,对偶Riesz变换记为T1^＊=（-△＋V）^（-1）V和T2^＊=（-△＋V）^（-1/2）V^（-1/2）.本文建立了T1^＊和T2^＊以及他们的交换子在与位势V∈Bq,q≥n/2相关的加权Morrey空间L（α,V,ω）^（p,λ）（R^n）上的有界性.这些结果实质性地推广了一些已知的结果.作为应用,本文的结果可以应用于Hermite算子的情形.

英文摘要：

Let L =-△＋ V be a Schr？dinger operator,where A is the Laplacian on R^n and the nonnegative potential V belongs to the reverse H？lder class Bq for q ≥n/2.The Riesz transforms associated with the operator L are denoted by T1 = V（-△ ＋ V）^（-1） and T2 =V^（-1/2）（-△ ＋ V）^（-1/2） and the dual Riesz transforms are denoted by T1^＊ =（-△ ＋ V）^（-1）V and T2^＊ =（-△ ＋ K）^（-1/2）V^（-1/2）.In this paper,we establish the boundedness for the operator T1^＊ and T2^＊ and their commutators on weighted Morrey spaces L（α,V,ω）^（p,λ）（R^n） associated with the potential V ∈ Bq for q ≥ n/2.These results generalize substantially some well-known results.As an application,we can apply our results to the case of Hermite operators.