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

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-Δ_Hⁿ+V，其中Δ_Hⁿ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B_q1。我们将证明算子T=V^a(-Δ+V)^-a在H_L¹(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 -Δ_Hⁿ+V, where Δ_Hⁿ is the sub-Laplacian and the non-  negative potential V belongs to the reverse Hölder class B_q1 for q₁>Q/2. We show that the operator T=V^a(-Δ+V)^-a is bounded from H_L¹(Hⁿ) to L¹(Hⁿ).