标题:
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
关键字:
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
期刊名称:
《Pure Mathematics》, Vol.5 No.6, 2015-11-30
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。
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).