Ni Tianzhen, Liu Yu
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, China.
J Inequal Appl. 2017;2017(1):312. doi: 10.1186/s13660-017-1584-8. Epub 2017 Dec 19.
Assume that is a nilpotent Lie group. Denote by [Formula: see text] the Schrödinger operator on , where Δ is the sub-Laplacian, the nonnegative potential belongs to the reverse Hölder class [Formula: see text] for some [Formula: see text] and is the dimension at infinity of . Let [Formula: see text] be the Riesz transform associated with . In this paper we obtain some estimates for the commutator [Formula: see text] for [Formula: see text], where [Formula: see text] is a function space which is larger than the classical Lipschitz space.
假设(G)是一个幂零李群。用(L = -\Delta + V)表示(G)上的薛定谔算子，其中(\Delta)是次拉普拉斯算子，非负势函数(V)对于某个(q > 1)属于反向赫尔德类(RH_q)，且(Q)是(G)的无穷维数。设(R_j)是与(\Delta)相关的里斯变换。在本文中，我们得到了对于(b \in \mathcal{M}\beta (G))，换位子([b, R_j])的一些估计，其中(\mathcal{M}\beta (G))是一个比经典利普希茨空间更大的函数空间。
