Volume 32, Issue 1
Hardy Type Estimates for Riesz Transforms Associated with Schrödinger Operators on the Heisenberg Group

Y. Liu and G. B. Tang

10.4208/ata.2016.v32.n1.7

Anal. Theory Appl., 32 (2016), pp. 78-89.

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  • Abstract

Let Hn be the Heisenberg group and Q=2n+2 be its homogeneous dimension. In this paper, we consider the Schr ¨odinger operator −∆Hn +V, where ∆Hn is the sub-Laplacian and V is the nonnegative potential belonging to the reverse H ¨older class Bq1for q1 ≥ Q/2. We show that the operators T1 = V(−∆Hn +V)−1 and T2 = V1/2(−∆Hn +V)−1/2 are both bounded from H1L(Hn) into L1(Hn). Our results are also valid on the stratified Lie group.

  • History

Published online: 2016-01

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