Uniform resolvent estimates for Schrödinger operator with an inverse-square potential

Haruya Mizutani; Junyong Zhang; Jiqiang Zheng

doi:10.1016/j.jfa.2019.108350

Uniform resolvent estimates for Schrödinger operator with an inverse-square potential

Haruya Mizutani, Junyong Zhang^*, Jiqiang Zheng

^*Corresponding author for this work

School of Mathematics and Statistics

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

9 Citations (Scopus)

Abstract

We study the uniform resolvent estimates for Schrödinger operator with a Hardy-type singular potential. Let L_V=−Δ+V(x) where Δ is the usual Laplacian on Rⁿ and V(x)=V₀(θ)r⁻² where r=|x|,θ=x/|x| and V₀(θ)∈C¹(Sⁿ⁻¹) is a real function such that the operator −Δ_θ+V₀(θ)+(n−2)²/4 is a strictly positive operator on L²(Sⁿ⁻¹). We prove some new uniform weighted resolvent estimates and also obtain some uniform Sobolev estimates associated with the operator L_V.

Original language	English
Article number	108350
Journal	Journal of Functional Analysis
Volume	278
Issue number	4
DOIs	https://doi.org/10.1016/j.jfa.2019.108350
Publication status	Published - 1 Mar 2020

Keywords

Inhomogeneous Strichartz estimate
Inverse-square potential
Sobolev inequality
Uniform resolvent estimate

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10.1016/j.jfa.2019.108350

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title = "Uniform resolvent estimates for Schr{\"o}dinger operator with an inverse-square potential",

abstract = "We study the uniform resolvent estimates for Schr{\"o}dinger operator with a Hardy-type singular potential. Let LV=−Δ+V(x) where Δ is the usual Laplacian on Rn and V(x)=V0(θ)r−2 where r=|x|,θ=x/|x| and V0(θ)∈C1(Sn−1) is a real function such that the operator −Δθ+V0(θ)+(n−2)2/4 is a strictly positive operator on L2(Sn−1). We prove some new uniform weighted resolvent estimates and also obtain some uniform Sobolev estimates associated with the operator LV.",

keywords = "Inhomogeneous Strichartz estimate, Inverse-square potential, Sobolev inequality, Uniform resolvent estimate",

author = "Haruya Mizutani and Junyong Zhang and Jiqiang Zheng",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2020",

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doi = "10.1016/j.jfa.2019.108350",

language = "English",

volume = "278",

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T1 - Uniform resolvent estimates for Schrödinger operator with an inverse-square potential

AU - Mizutani, Haruya

AU - Zhang, Junyong

AU - Zheng, Jiqiang

PY - 2020/3/1

Y1 - 2020/3/1

N2 - We study the uniform resolvent estimates for Schrödinger operator with a Hardy-type singular potential. Let LV=−Δ+V(x) where Δ is the usual Laplacian on Rn and V(x)=V0(θ)r−2 where r=|x|,θ=x/|x| and V0(θ)∈C1(Sn−1) is a real function such that the operator −Δθ+V0(θ)+(n−2)2/4 is a strictly positive operator on L2(Sn−1). We prove some new uniform weighted resolvent estimates and also obtain some uniform Sobolev estimates associated with the operator LV.

AB - We study the uniform resolvent estimates for Schrödinger operator with a Hardy-type singular potential. Let LV=−Δ+V(x) where Δ is the usual Laplacian on Rn and V(x)=V0(θ)r−2 where r=|x|,θ=x/|x| and V0(θ)∈C1(Sn−1) is a real function such that the operator −Δθ+V0(θ)+(n−2)2/4 is a strictly positive operator on L2(Sn−1). We prove some new uniform weighted resolvent estimates and also obtain some uniform Sobolev estimates associated with the operator LV.

KW - Inhomogeneous Strichartz estimate

KW - Inverse-square potential

KW - Sobolev inequality

KW - Uniform resolvent estimate

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U2 - 10.1016/j.jfa.2019.108350

DO - 10.1016/j.jfa.2019.108350

M3 - Article

AN - SCOPUS:85073532838

SN - 0022-1236

VL - 278

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 4

M1 - 108350

ER -

Uniform resolvent estimates for Schrödinger operator with an inverse-square potential

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