Hardy Type Estimates for Riesz Transforms Associated with Schrdinger Operators on the Heisenberg Group  

作　　者：Yu Liu Guobin Tang 

机构地区：[1]School of Mathematics and Physics, University of Science and Technology Beijing,Beijing 100083, China

出　　处：《Analysis in Theory and Applications》2016年第1期78-89,共12页分析理论与应用（英文刊）

摘　　要：Abstract. Let H^n be the Heisenberg group and Q = 2n＋2 be its homogeneous dimen- sion. In this paper, we consider the Schr6dinger operator -△H^n ＋V, where △H^n is the sub-Laplacian and V is the nonnegative potential belonging to the reverse H61der class Bql for ql _〉 Q/2. We show that the operators T1 = V（-△H^n-In ＋V）-1 and T2 = V1/2（-△H^n-V）-1/2 are both bounded from 1 n HL^1（H^n ） into L1（H^n）. Our results are also valid on the stratified Lie group.Abstract. Let H^n be the Heisenberg group and Q = 2n＋2 be its homogeneous dimen- sion. In this paper, we consider the Schr6dinger operator -△H^n ＋V, where △H^n is the sub-Laplacian and V is the nonnegative potential belonging to the reverse H61der class Bql for ql _〉 Q/2. We show that the operators T1 = V（-△H^n-In ＋V）-1 and T2 = V1/2（-△H^n-V）-1/2 are both bounded from 1 n HL^1（H^n ） into L1（H^n）. Our results are also valid on the stratified Lie group.

关 键 词：Heisenberg group stratified Lie group reverse H61der class Riesz transform Schr6dinger operator. 

分 类 号：O152[理学—数学]