Spectral Multipliers for Magnetic Schrödinger Operators

Shijun Zheng

doi:10.1007/s44007-024-00102-4

Spectral Multipliers for Magnetic Schrödinger Operators

Shijun Zheng

Mathematical Sciences

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

Abstract

In this paper, we prove some spectral multiplier theorems for a self-adjoint operator H on Besov and Triebel–Lizorkin type spaces. This allows to give norm characterization of the perturbed Sobolev and Besov spaces associated with H. As an application, we obtain the local well posedness and uniqueness for the solutions to dispersive equations with certain magnetic potentials.

Original language	English
Journal	Matematica
DOIs	https://doi.org/10.1007/s44007-024-00102-4
State	Accepted/In press - 2024

Keywords

35Q40
42B25
Besov and Triebel–Lizorkin spaces
Dispersive equation
Littlewood–Paley decomposition
Magnetic Schrödinger operator
Primary 35J10
Secondary 35P25
Spectral multiplier

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10.1007/s44007-024-00102-4

Cite this

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title = "Spectral Multipliers for Magnetic Schr{\"o}dinger Operators",

abstract = "In this paper, we prove some spectral multiplier theorems for a self-adjoint operator H on Besov and Triebel–Lizorkin type spaces. This allows to give norm characterization of the perturbed Sobolev and Besov spaces associated with H. As an application, we obtain the local well posedness and uniqueness for the solutions to dispersive equations with certain magnetic potentials.",

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author = "Shijun Zheng",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.",

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language = "English",

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T1 - Spectral Multipliers for Magnetic Schrödinger Operators

AU - Zheng, Shijun

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

PY - 2024

Y1 - 2024

N2 - In this paper, we prove some spectral multiplier theorems for a self-adjoint operator H on Besov and Triebel–Lizorkin type spaces. This allows to give norm characterization of the perturbed Sobolev and Besov spaces associated with H. As an application, we obtain the local well posedness and uniqueness for the solutions to dispersive equations with certain magnetic potentials.

AB - In this paper, we prove some spectral multiplier theorems for a self-adjoint operator H on Besov and Triebel–Lizorkin type spaces. This allows to give norm characterization of the perturbed Sobolev and Besov spaces associated with H. As an application, we obtain the local well posedness and uniqueness for the solutions to dispersive equations with certain magnetic potentials.

KW - 35Q40

KW - 42B25

KW - Besov and Triebel–Lizorkin spaces

KW - Dispersive equation

KW - Littlewood–Paley decomposition

KW - Magnetic Schrödinger operator

KW - Primary 35J10

KW - Secondary 35P25

KW - Spectral multiplier

UR - http://www.scopus.com/inward/record.url?scp=85198624768&partnerID=8YFLogxK

U2 - 10.1007/s44007-024-00102-4

DO - 10.1007/s44007-024-00102-4

M3 - Article

AN - SCOPUS:85198624768

SN - 2730-9657

JO - Matematica

JF - Matematica

ER -

Spectral Multipliers for Magnetic Schrödinger Operators

Abstract

Keywords

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