具有非负位势的薛定谔型算子的估计

数学物理学报 ›› 2011, Vol. 31 ›› Issue (3): 611-619.

具有非负位势的薛定谔型算子的估计

刘宇

北京科技大学数理学院数学力学系北京 100083

收稿日期:2009-08-22 修回日期:2010-08-19 出版日期:2011-06-25 发布日期:2011-06-25
基金资助:
国家自然科学基金(10901018) 和北京科技大学冶金工程研究院理论研究基金(00009503)资助

An Estimate for the Schr¨odinger Type Operators with Certain Nonnegative Potentials

LIU Yu

Department of Mathematics and Mechanics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083

Received:2009-08-22 Revised:2010-08-19 Online:2011-06-25 Published:2011-06-25
Supported by:
国家自然科学基金(10901018) 和北京科技大学冶金工程研究院理论研究基金(00009503)资助

摘要/Abstract

摘要：

令L=-Δ+V是欧氏空间R^d上具有非负多项式位势的薛定谔算子. BMO_L(R^d) 是与薛定谔算子相关的哈代型空间H¹_L(R^d )的对偶空间. 该文证明当位势V是非负多项式时, 薛定谔型算子(−Δ + V )^−β∇是从L^p(R^d) 到BMO_L(R^d)的有界线性算子, 其中p =d/2β-1.

关键词: BMO_L(R^d), 薛定谔算子, 逆Hölder 类

Abstract:

Let L = −Δ+ V be the Schr¨odinger operator on Rd with the potential V being a nonnegative polynomial. BMO_L(R^d) is a dual space of the Hardy-type space H¹ _L(R^d) related to Schr¨odinger operator L = −Δ+V . In this article it is proved that the Schr¨odinger type operator (−Δ+ V )^−β∇ is bounded from L^p(R^d) into BMO_L(R^d) for p = d/2β−1 when the potential V is a nonnegative polynomial.

Key words: BMO_L(R^d), Schr¨odinger operators, Reverse Hölder class

中图分类号:

35J10

刘宇. 具有非负位势的薛定谔型算子的估计[J]. 数学物理学报, 2011, 31(3): 611-619.

LIU Yu. An Estimate for the Schr¨odinger Type Operators with Certain Nonnegative Potentials[J]. Acta mathematica scientia,Series A, 2011, 31(3): 611-619.

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