@Article{ATA-36-99, author = {Wang , Yueshan}, 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 = {

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 $q_1> n/2, n\geq 5.$ 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 $1/q=1/p-m\beta/n.$

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2017-0055}, url = {http://global-sci.org/intro/article_detail/ata/16917.html} }