Bounds on the maximal bochner-riesz means for elliptic operators

Peng Chen; Sanghyuk Lee; Adam Sikora; Lixin Yan

doi:10.1090/tran/8024

Bounds on the maximal bochner-riesz means for elliptic operators

Peng Chen^*, Sanghyuk Lee, Adam Sikora, Lixin Yan

^*Corresponding author for this work

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Abstract

We investigate Lp boundedness of the maximal Bochner-Riesz means for self-adjoint operators of elliptic-type. Assuming the finite speed of propagation for the associated wave operator, from the restriction-type estimates we establish the sharp Lp boundedness of the maximal Bochner-Riesz means for the elliptic operators. As applications, we obtain the sharp Lp maximal bounds for the Schrödinger operators on asymptotically conic manifolds, elliptic operators on compact manifolds, or the Hermite operator and its perturbations on ℝⁿ .

Original language	English
Pages (from-to)	3793-3828
Number of pages	36
Journal	Transactions of the American Mathematical Society
Volume	373
Issue number	6
Early online date	2 Mar 2020
DOIs	https://doi.org/10.1090/tran/8024
Publication status	Published - Jun 2020

Keywords

Maximal Bochner-Riesz means
non-negative self-adjoint operators
finite speed propagation property
elliptic-type estimates
restriction-type conditions

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10.1090/tran/8024

Accepted author manuscriptAccepted author manuscript, 324 KBLicence: CC BY-NC-ND

Cite this

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title = "Bounds on the maximal bochner-riesz means for elliptic operators",

abstract = "We investigate Lp boundedness of the maximal Bochner-Riesz means for self-adjoint operators of elliptic-type. Assuming the finite speed of propagation for the associated wave operator, from the restriction-type estimates we establish the sharp Lp boundedness of the maximal Bochner-Riesz means for the elliptic operators. As applications, we obtain the sharp Lp maximal bounds for the Schr{\"o}dinger operators on asymptotically conic manifolds, elliptic operators on compact manifolds, or the Hermite operator and its perturbations on ℝn .",

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AU - Chen, Peng

AU - Lee, Sanghyuk

AU - Sikora, Adam

AU - Yan, Lixin

PY - 2020/6

Y1 - 2020/6

N2 - We investigate Lp boundedness of the maximal Bochner-Riesz means for self-adjoint operators of elliptic-type. Assuming the finite speed of propagation for the associated wave operator, from the restriction-type estimates we establish the sharp Lp boundedness of the maximal Bochner-Riesz means for the elliptic operators. As applications, we obtain the sharp Lp maximal bounds for the Schrödinger operators on asymptotically conic manifolds, elliptic operators on compact manifolds, or the Hermite operator and its perturbations on ℝn .

AB - We investigate Lp boundedness of the maximal Bochner-Riesz means for self-adjoint operators of elliptic-type. Assuming the finite speed of propagation for the associated wave operator, from the restriction-type estimates we establish the sharp Lp boundedness of the maximal Bochner-Riesz means for the elliptic operators. As applications, we obtain the sharp Lp maximal bounds for the Schrödinger operators on asymptotically conic manifolds, elliptic operators on compact manifolds, or the Hermite operator and its perturbations on ℝn .

KW - Maximal Bochner-Riesz means

KW - non-negative self-adjoint operators

KW - finite speed propagation property

KW - elliptic-type estimates

KW - restriction-type conditions

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UR - http://purl.org/au-research/grants/arc/DP160100941

UR - http://purl.org/au-research/grants/arc/DP170101060

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DO - 10.1090/tran/8024

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SN - 0002-9947

VL - 373

SP - 3793

EP - 3828

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 6

ER -

Bounds on the maximal bochner-riesz means for elliptic operators

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Keywords

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Harmonic analysis and dispersive partial differential equations

Harmonic analysis of rough oscillations

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Bounds on the maximal bochner-riesz means for elliptic operators

Abstract

Keywords

Access to Document

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Harmonic analysis and dispersive partial differential equations

Harmonic analysis of rough oscillations

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