# Commutators associated with Schrödinger operators on the nilpotent Lie group

@article{Ni2017CommutatorsAW,
title={Commutators associated with Schr{\"o}dinger operators on the nilpotent Lie group},
author={Tianzhen Ni and Yu Liu},
journal={Journal of Inequalities and Applications},
year={2017},
volume={2017}
}
• Published 2017
• Mathematics, Medicine
• Journal of Inequalities and Applications
• Assume that G is a nilpotent Lie group. Denote by L=−Δ+W$L=-\Delta +W$ the Schrödinger operator on G, where Δ is the sub-Laplacian, the nonnegative potential W belongs to the reverse Hölder class Bq1$B_{q_{1}}$ for some q1≥D2$q_{1} \geq \frac{D}{2}$ and D is the dimension at infinity of G. Let R=∇(−Δ+W)−12$\mathcal{R}=\nabla (-\Delta +W)^{-\frac{1}{2}}$ be the Riesz transform associated with L. In this paper we obtain some estimates for the commutator [h,R]$[h,\mathcal{R}]$ for h∈Lipνθ\$h\in… CONTINUE READING

#### References

SHOWING 1-10 OF 15 REFERENCES
DC: Maximal function characterizations of Hardy spaces associated with Schrödinger operators on nilpotent Lie groups
• Rev. Mat. Complut
• 2011
Localized Hardy spaces H1 related to admissible functions on RD-spaces and applications to Schrödinger operators
• Trans. Am. Math. Soc. 363, 1197-1239
• 2011
O: Two-weight norm inequalities for the fractional maximal operator on spaces of homogeneous type
• Stud. Math
• 1994