Lp ESTIMATES FOR SCHRÖDINGER TYPE OPERATORS ON THE HEISENBERG GROUP

Title & Authors
Lp ESTIMATES FOR SCHRÖDINGER TYPE OPERATORS ON THE HEISENBERG GROUP
Yu, Liu;

Abstract
We investigate the Schr$\small{\ddot{o}}$dinger type operator $\small{H_2\;=\;(-\Delta_{\mathbb{H}^n})^2+V^2}$ on the Heisenberg group $\small{\mathbb{H}^n}$, where $\small{\Delta_{\mathbb{H}^n}}$ is the sublaplacian and the nonnegative potential V belongs to the reverse H$\small{\ddot{o}}$lder class $\small{B_q}$ for $\small{q\geq\frac{Q}{2}}$, where Q is the homogeneous dimension of $\small{\mathbb{H}^n}$. We shall establish the estimates of the fundamental solution for the operator $\small{H_2}$ and obtain the $\small{L^p}$ estimates for the operator $\small{\nabla^4_{\mathbb{H}^n}H^{-1}_2}$, where $\small{\nabla_{\mathbb{H}^n}}$ is the gradient operator on $\small{\mathbb{H}^n}$.
Keywords
Heisenberg group;Schr$\small{\ddot{o}}$dinger operators;reverse H$\small{\ddot{o}}$lder class;
Language
English
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4.
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