海森堡群上与薛定谔算子相关的里斯变换的哈代型估计
Hardy Type Estimates for Riesz Transforms Associated with Schr?dinger Operators on the Heisenberg Group
DOI: 10.12677/PM.2015.56042, PDF,  被引量    国家自然科学基金支持
作者: 汤国斌, 刘 宇*：北京科技大学数理学院，北京
关键词: 海森堡群；逆赫尔德类；里斯变换；薛定谔算子；Heisenberg Group； Reverse H?lder Class； Riesz Transform； Schr?dinger Operators
摘要: 令Hn为海森堡群，Q=2n+2为其齐次维数。本文考虑了薛定谔算子-ΔHn+V，其中ΔHn为次拉普拉斯算子，对于q1>Q/2，非负位势V属于逆赫尔德类Bq1。我们将证明算子T=Va(-Δ+V)-a在HL1(Hn)到L1(Hn)上是有界的。
Abstract: Let Hn be the Heisenberg group and Q=2n+2 be its homogenous dimension. In this paper, we consider the Schrödinger operator -ΔHn+V, where ΔHn is the sub-Laplacian and the non-  negative potential V belongs to the reverse Hölder class Bq1 for q1>Q/2. We show that the operator T=Va(-Δ+V)-a is bounded from HL1(Hn) to L1(Hn).
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. https://dx.doi.org/10.12677/PM.2015.56042

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