Heisenberg群上与Schrdinger算子相关的Riesz变换(英文)

Riesz Transform Associated With Schrdinger Operators on the Heisenberg Group

本文考虑了Heisenberg群H^n上的Schrdinger算子-△_(H^n)+V,其中△_(H^n)是次拉普拉斯算子以及对于q≥Q/2和Q是H^n的齐次维数,非负位势V属于逆Hlder类B_q.主要结果是证明如果q=Q,Riesz变换▽_(H^n)(-△_(H^n)+V)^(-1/2)是Calderon-Zygmund算子,其中▽_(H^n)是H^n上的梯度算子.

In this paper we consider the Schrodinger operators -△_H^n ＋ V on the Heisenberg group H^n where△_H^n is the sublaplacian and the nonnegative potential V belongs to the reverse Holder class B^q for q≥Q/2 where Q is the homogeneous dimension of H^n.Our main result is to prove that the Riesz transform▽_H^n（-△_H^n ＋ V）^（-1/2） is Calderon-Zygmund operator if q = Q,where▽_H^n is the gradient operator on H^n.