Boundedness of High Order Commutators of Riesz Transforms Associated with Schrödinger Type Operators
Year: 2020
Author: Yueshan Wang
Analysis in Theory and Applications, Vol. 36 (2020), Iss. 1 : pp. 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 $1/q=1/p-m\beta/n.$
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2017-0055
Analysis in Theory and Applications, Vol. 36 (2020), Iss. 1 : pp. 99–110
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Schrödinger operator Campanato space Riesz transform commutator.