Estimates for the higher order Riesz transforms related to Schr\"odinger type operators
Bull. Korean Math. Soc. 2021 Vol. 58, No. 1, 235-251
Published online November 3, 2020
Printed January 31, 2021
Yanhui Wang
Jiaozuo University
Abstract : We consider the Schr\"odinger type operator \(\mathcal{L}_k=(-\Delta)^k+V^k \) on \(\mathbb{R}^n ( n\geq 2k+1)\), where \(k=1,2\) and the nonnegative potential \(V\) belongs to the reverse H\"older class \(RH_s\) with \( n/21/2,$ where $p_1=\frac{n}{4(\beta-\alpha)-2}$, $p_2=\frac{n}{n-4(\beta-\alpha)+2}.$ Moreover, we prove that $T_{\alpha,\beta}$ is bounded from $BMO_{\mathcal{L}_1}(\mathbb{R}^n)$ to itself when $\beta-\alpha=1/2.$
Keywords : Riesz transform, Schr\"odinger operator, Hardy space, BMO
MSC numbers : Primary 35J10, 42B35
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