Commutators associated with Schrödinger operators on the nilpotent Lie group

  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},
  • Tianzhen Ni, Yu Liu
  • 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

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