Year: 2018
Analysis in Theory and Applications, Vol. 34 (2018), Iss. 1 : pp. 45–76
Abstract
Let $A:=−(\nabla−i\vec{a})·(\nabla−i\vec{a})+V$ be a magnetic Schrödinger operator on $L^2(\mathbb{R}^n)$, $n\geq 2$, where $\vec{a} := (a_1
,···,a_n) \in L^2_{loc}(\mathbb{R^n}, \mathbb{R^n})$ and $0\leq V \in L^1_{loc}(\mathbb{R^n})$. In this paper, we
show that for a function $b$ in Lipschitz space Lip$_{\alpha}$ $(\mathbb{R^n})$ with $\alpha\in (0,1)$, the commutator $[b, V^{1/2}A^{-1/2}]$ is bounded from $L^p(\mathbb{R^n})$ to $L^q(\mathbb{R^n})$, where $p$, $q\in (1,2]$ and $1/p−1/q =
α/n$.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2018.v34.n1.4
Analysis in Theory and Applications, Vol. 34 (2018), Iss. 1 : pp. 45–76
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Commutator Lipschitz space the sharp maxical function magnetic Schrödinger operator Hölder inequality.