@Article{ATA-36-1,
author = {Yueshan, Wang},
title = {Boundedness of  High Order Commutators of Riesz Transforms Associated with  Schrödinger Type Operators},
journal = {Analysis in Theory and Applications},
year = {2020},
volume = {36},
number = {1},
pages = {99--110},
abstract = {<p style="text-align: justify;">Let $\mathcal{L}_2=(-\Delta)^2+V^2$ be the Schrödinger type operator, where $V\neq 0$ is a nonnegative potential and belongs to the reverse Hölder class $RH_{q_1}$ for $q_1&gt; n/2, n\geq 5.$ The higher Riesz transform associated with $\mathcal{L}_2$ is denoted by $\mathcal{R}=\nabla^2 \mathcal{L}_2^{-\frac{1}{2}}$ and its dual is denoted by $\mathcal{R}^*=\mathcal{L}_2^{-\frac{1}{2}} \nabla^2.$ In this paper, we consider the $m$-order commutators $[b^m,\mathcal{R}]$ and $[b^m,\mathcal{R}^*],$ and establish the $(L^p,L^q)$-boundedness of these commutators when $b$ belongs to the new Campanato space $\Lambda_\beta^\theta(\rho)$ and $1/q=1/p-m\beta/n.$</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.OA-2017-0055},
url = {https://global-sci.com/article/73803/boundedness-of-high-order-commutators-of-riesz-transforms-associated-with-schrodinger-type-operators}
}