Weighted norm inequalities for riesz transforms of magnetic Schr̈odinger operators

Bui The Anh

Weighted norm inequalities for riesz transforms of magnetic Schr̈odinger operators

Bui The Anh^*

^*Corresponding author for this work

Faculty of Science and Engineering

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

Let A = -(r i→a)² + V be a magnetic Schrödinger operator acting on L²(Rⁿ), n ≥ 1, where →a = (a1,..., a_n) ∈ L² _loc and 0 ≤ V ∈ L¹ _loc. In this paper we will give weighted L^p estimates for Riesz transforms (δ=δx_k - iak)A ^-1/2 associated with A, k = 1,..., n, and their commutators with an appropriate range of p. Note that our obtained results extend those in [11, 12].

Original language	English
Pages (from-to)	811-826
Number of pages	16
Journal	Differential and Integral Equations
Volume	23
Issue number	9-10
Publication status	Published - Sep 2010

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title = "Weighted norm inequalities for riesz transforms of magnetic Sch{\"r}odinger operators",

abstract = "Let A = -(r i→a)2 + V be a magnetic Schr{\"o}dinger operator acting on L2(Rn), n ≥ 1, where →a = (a1,..., an) ∈ L2 loc and 0 ≤ V ∈ L1 loc. In this paper we will give weighted Lp estimates for Riesz transforms (δ=δxk - iak)A -1/2 associated with A, k = 1,..., n, and their commutators with an appropriate range of p. Note that our obtained results extend those in [11, 12].",

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year = "2010",

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language = "English",

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journal = "Differential and Integral Equations",

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T1 - Weighted norm inequalities for riesz transforms of magnetic Schr̈odinger operators

AU - Anh, Bui The

PY - 2010/9

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N2 - Let A = -(r i→a)2 + V be a magnetic Schrödinger operator acting on L2(Rn), n ≥ 1, where →a = (a1,..., an) ∈ L2 loc and 0 ≤ V ∈ L1 loc. In this paper we will give weighted Lp estimates for Riesz transforms (δ=δxk - iak)A -1/2 associated with A, k = 1,..., n, and their commutators with an appropriate range of p. Note that our obtained results extend those in [11, 12].

AB - Let A = -(r i→a)2 + V be a magnetic Schrödinger operator acting on L2(Rn), n ≥ 1, where →a = (a1,..., an) ∈ L2 loc and 0 ≤ V ∈ L1 loc. In this paper we will give weighted Lp estimates for Riesz transforms (δ=δxk - iak)A -1/2 associated with A, k = 1,..., n, and their commutators with an appropriate range of p. Note that our obtained results extend those in [11, 12].

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M3 - Article

AN - SCOPUS:84875375154

VL - 23

SP - 811

EP - 826

JO - Differential and Integral Equations

JF - Differential and Integral Equations

SN - 0893-4983

IS - 9-10

ER -

Weighted norm inequalities for riesz transforms of magnetic Schr̈odinger operators

Abstract

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