Differential and Integral Equations

Weighted norm inequalities for Riesz transforms of magnetic Schrödinger operators

Bui The Anh

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Abstract

Let $A=-(\nabla-i\vec{a})^2+V$ be a magnetic Schrödinger operator acting on $L^2(\mathbb{R}^n), n\geq 1$, where $\vec{a}=(a_1,\ldots, a_n)\in L^2_{loc}$ and $0\leq V \in L^1_{ loc}$. In this paper we will give weighted $L^p$ estimates for Riesz transforms $(\partial/\partial x_k -ia_k )A^{-1/2}$ associated with $A, k=1, \ldots, n,$ and their commutators with an appropriate range of $p$. Note that our obtained results extend those in [11, 12].

Article information

Source
Differential Integral Equations, Volume 23, Number 9/10 (2010), 811-826.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019114

Mathematical Reviews number (MathSciNet)
MR2675584

Zentralblatt MATH identifier
1240.42034

Subjects
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory 47B38: Operators on function spaces (general)

Citation

Anh, Bui The. Weighted norm inequalities for Riesz transforms of magnetic Schrödinger operators. Differential Integral Equations 23 (2010), no. 9/10, 811--826. https://projecteuclid.org/euclid.die/1356019114


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