@Article{ATA-34-45,
author = {Wanqing Ma and Yu Liu},
title = {Commutators of Singular Integral Operators Related to Magnetic Schrödinger Operators},
journal = {Analysis in Theory and Applications},
year = {2018},
volume = {34},
number = {1},
pages = {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 $1/p−1/q =
α/n$.
},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.2018.v34.n1.4},
url = {http://global-sci.org/intro/article_detail/ata/12544.html}
}
TY - JOUR
T1 - Commutators of Singular Integral Operators Related to Magnetic Schrödinger Operators
AU - Wanqing Ma & Yu Liu
JO - Analysis in Theory and Applications
VL - 1
SP - 45
EP - 76
PY - 2018
DA - 2018/07
SN - 34
DO - http://doi.org/10.4208/ata.2018.v34.n1.4
UR - https://global-sci.org/intro/article_detail/ata/12544.html
KW - Commutator, Lipschitz space, the sharp maxical function, magnetic Schrödinger operator, Hölder inequality.
AB -
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 $1/p−1/q =
α/n$.
Wanqing Ma and Yu Liu. (2018). Commutators of Singular Integral Operators Related to Magnetic Schrödinger Operators.
Analysis in Theory and Applications. 34 (1).
45-76.
doi:10.4208/ata.2018.v34.n1.4
