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

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 (2015) 海森堡群上与薛定谔算子相关的里斯变换的哈代型估计。 理论数学, 5, 291-297. doi: 10.12677/PM.2015.56042

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