The Boundedness Of Commutators Generated By Riesz Transform Associated With Schr(?)dinger Operator

Schr(o|¨)dinger operator is the extension of the elliptic partial differential equations operator,and the boundedness of commutators generated by Riesz transform associated with it and BMO type functions is the key point of this paper.This paper also studies the character of kernel when the smoothness of kernel is weaked to condition H(m) and the boundedness of commutator at that condition and the boundedness of commutators generated by Riesz transform associated with Schr(o|¨)dinger operator and Lipschitz functions.And there are five parts in this paper.In charpter 1,the paper simply introduces the background and development of the Schr(o|¨)dinger operators,Riesz transform associated with it and Hardy space.In chapter 2,it discusses the weak type estimate and H_b^p boundedness of commutators generated by Riesz transform associated with Schr(o|¨)dinger operators and BMO_A functions.It is proved that if p and potential V(x)satisfies certain condition, then the estimates and the boundednss exist.In chapter 3,it discusses the H_b¹ boundedness of commutators generated by Riesz transform associated with Schr(o|¨)dinger operators and BMO functions when operators dissatisfy smoothness.In chapter 4,the paper studies the boundedness of commutators generated by Riesz transform associated with Schr(o|¨)dinger operators and(?)_βfunctions.And it is proved the commutators' boundedness of L^p→(?)_p^β,∞(Rⁿ)and L^p(Rⁿ)→L^q(Rⁿ).In chapter 5,the conclusions and prospects of this paper are presented.