Resolvent estimates for Schrödinger operators with potentials in Lebesgue spaces

Tianyi Ren

doi:10.1016/j.jmaa.2020.124590

Resolvent estimates for Schrödinger operators with potentials in Lebesgue spaces

Tianyi Ren

Peking University

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

Abstract

We prove resolvent estimates in the Euclidean setting for Schrödinger operators with potentials in Lebesgue spaces: −Δ+V. The (L²,L^p) estimates were already obtained by Blair-Sogge-Sire, but we extend their result to other (L^p,L^q) estimates using their idea and the result and method of Kwon-Lee on non-uniform resolvent estimates in the Euclidean space.

Original language	English
Article number	124590
Journal	Journal of Mathematical Analysis and Applications
Volume	494
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2020.124590
State	Published - 1 Feb 2021
Externally published	Yes

Keywords

Resolvent estimates
Schrodinger operators with potentials

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10.1016/j.jmaa.2020.124590

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title = "Resolvent estimates for Schr{\"o}dinger operators with potentials in Lebesgue spaces",

abstract = "We prove resolvent estimates in the Euclidean setting for Schr{\"o}dinger operators with potentials in Lebesgue spaces: −Δ+V. The (L2,Lp) estimates were already obtained by Blair-Sogge-Sire, but we extend their result to other (Lp,Lq) estimates using their idea and the result and method of Kwon-Lee on non-uniform resolvent estimates in the Euclidean space.",

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author = "Tianyi Ren",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2021",

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AU - Ren, Tianyi

PY - 2021/2/1

Y1 - 2021/2/1

N2 - We prove resolvent estimates in the Euclidean setting for Schrödinger operators with potentials in Lebesgue spaces: −Δ+V. The (L2,Lp) estimates were already obtained by Blair-Sogge-Sire, but we extend their result to other (Lp,Lq) estimates using their idea and the result and method of Kwon-Lee on non-uniform resolvent estimates in the Euclidean space.

AB - We prove resolvent estimates in the Euclidean setting for Schrödinger operators with potentials in Lebesgue spaces: −Δ+V. The (L2,Lp) estimates were already obtained by Blair-Sogge-Sire, but we extend their result to other (Lp,Lq) estimates using their idea and the result and method of Kwon-Lee on non-uniform resolvent estimates in the Euclidean space.

KW - Resolvent estimates

KW - Schrodinger operators with potentials

UR - https://www.scopus.com/pages/publications/85091121888

U2 - 10.1016/j.jmaa.2020.124590

DO - 10.1016/j.jmaa.2020.124590

M3 - 文章

AN - SCOPUS:85091121888

SN - 0022-247X

VL - 494

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

M1 - 124590

ER -

Resolvent estimates for Schrödinger operators with potentials in Lebesgue spaces

Abstract

Keywords

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