Hardy Type Estimates for Riesz Transforms Associated with Schrödinger Operators on the Heisenberg Group
Year: 2016
Analysis in Theory and Applications, Vol. 32 (2016), Iss. 1 : pp. 78–89
Abstract
Let $\mathbb{H}^n$ be the Heisenberg group and $Q=2n+2$ be its homogeneous dimension. In this paper, we consider the Schrödinger operator $−∆_{\mathbb{H}^n} +V$, where $\Delta_{\mathbb{H}^n}$ is the sub-Laplacian and $V$ is the nonnegative potential belonging to the reverse Hölder class $B_{q_1}$ for $q_1 ≥ Q/2$. We show that the operators $T_1 = V(−∆_{\mathbb{H}^n} +V)^{−1}$ and $T_2 = V^{1/2}(−∆_{\mathbb{H}^n} +V)^{−1/2}$ are both bounded from $H^1_L(\mathbb{H}^n)$ into $L^1(\mathbb{H}^n)$. Our results are also valid on the stratified Lie group.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2016.v32.n1.7
Analysis in Theory and Applications, Vol. 32 (2016), Iss. 1 : pp. 78–89
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Heisenberg group stratified Lie group reverse Hölder class Riesz transform Schrödinger operator.
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A note for Riesz transforms associated with Schrödinger operators on the Heisenberg Group
Liu, Yu
Tang, Guobin
Analysis and Mathematical Physics, Vol. 7 (2017), Iss. 1 P.31
https://doi.org/10.1007/s13324-016-0128-6 [Citations: 4]