海森堡群上与薛定谔算子相关的里斯变换的哈 代型估计.pdfVIP

Pure Mathematics 理论数学, 2015, 5(6), 291-297 Published Online November 2015 in Hans. /journal/pm /10.12677/pm.2015.56042 Hardy Type Estimates for Riesz Transforms Associated with Schrödinger Operators on the Heisenberg Group Guobin Tang, Yu Liu* School of Mathematics and Physics, University of Science and Technology Beijing, Beijing th th th Received: Nov. 8 , 2015; accepted: Nov. 24 , 2015; published: Nov. 30 , 2015 Copyright © 2015 by authors and Hans Publishers Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). /licenses/by/4.0/ Abstract Let n be the Heisenberg group and Q 2n =+2 be its homogenous dimension. In this paper, we consider the Schrödinger operator −∆ +V , where ∆ is the sub-Laplacian and the non- n n negative potential V belongs to the reverse Hölder class Bq1 for q1 Q 2 . We show that the operator T Vα (=−∆+V )−α is bounded from H 1 n to L1 n . L ( ) ( ) Keywords Heisenberg Group, Reverse Hölder Class, Riesz Transform, Schrödinger Operators 海森堡群上与薛定谔算子相关的里斯变换的哈 代型估计 汤国斌，刘 宇* 北京科技大学数理学院，北京 *通讯作者。 文章引用: 汤国斌, 刘宇. 海森堡群上与薛定谔算子相关的里斯变换的哈代型估计[J]. 理论数学, 2015, 5(6): 291-297. /10.12677/pm.2015.56042 汤国斌，刘宇 收稿日期：2015年11月8 日；录用日期：2015年11月24 日；发布日期：2015年11月30 日 摘 要 n 令 为海森堡群， 为其齐次维数。本文考虑了薛定谔算子 ，其中 为次  Q 2n =+2 −∆ +V ∆