Linear adjoint restriction estimates for paraboloid

Changxing Miao; Junyong Zhang; Jiqiang Zheng

doi:10.1007/s00209-019-02251-7

Linear adjoint restriction estimates for paraboloid

Changxing Miao, Junyong Zhang^*, Jiqiang Zheng

^*Corresponding author for this work

School of Mathematics and Statistics

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

5 Citations (Scopus)

Abstract

We prove a class of modified paraboloid restriction estimates with a loss of angular derivatives for the full set of paraboloid restriction conjecture indices. This result generalizes the paraboloid restriction estimate in radial case from [Shao, Rev. Mat. Iberoam. 25(2009), 1127–1168], as well as the result from [Miao et al. Proc. AMS 140(2012), 2091–2102]. As an application, we show a local smoothing estimate for a solution of the linear Schrödinger equation under the assumption that the initial datum has additional angular regularity.

Original language	English
Pages (from-to)	427-451
Number of pages	25
Journal	Mathematische Zeitschrift
Volume	292
Issue number	1-2
DOIs	https://doi.org/10.1007/s00209-019-02251-7
Publication status	Published - 1 Jun 2019

Keywords

Bessel function
Linear adjoint restriction estimate
Local restriction estimate
Local smoothing
Spherical harmonics

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10.1007/s00209-019-02251-7

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title = "Linear adjoint restriction estimates for paraboloid",

abstract = "We prove a class of modified paraboloid restriction estimates with a loss of angular derivatives for the full set of paraboloid restriction conjecture indices. This result generalizes the paraboloid restriction estimate in radial case from [Shao, Rev. Mat. Iberoam. 25(2009), 1127–1168], as well as the result from [Miao et al. Proc. AMS 140(2012), 2091–2102]. As an application, we show a local smoothing estimate for a solution of the linear Schr{\"o}dinger equation under the assumption that the initial datum has additional angular regularity.",

keywords = "Bessel function, Linear adjoint restriction estimate, Local restriction estimate, Local smoothing, Spherical harmonics",

author = "Changxing Miao and Junyong Zhang and Jiqiang Zheng",

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T1 - Linear adjoint restriction estimates for paraboloid

AU - Miao, Changxing

AU - Zhang, Junyong

AU - Zheng, Jiqiang

PY - 2019/6/1

Y1 - 2019/6/1

N2 - We prove a class of modified paraboloid restriction estimates with a loss of angular derivatives for the full set of paraboloid restriction conjecture indices. This result generalizes the paraboloid restriction estimate in radial case from [Shao, Rev. Mat. Iberoam. 25(2009), 1127–1168], as well as the result from [Miao et al. Proc. AMS 140(2012), 2091–2102]. As an application, we show a local smoothing estimate for a solution of the linear Schrödinger equation under the assumption that the initial datum has additional angular regularity.

AB - We prove a class of modified paraboloid restriction estimates with a loss of angular derivatives for the full set of paraboloid restriction conjecture indices. This result generalizes the paraboloid restriction estimate in radial case from [Shao, Rev. Mat. Iberoam. 25(2009), 1127–1168], as well as the result from [Miao et al. Proc. AMS 140(2012), 2091–2102]. As an application, we show a local smoothing estimate for a solution of the linear Schrödinger equation under the assumption that the initial datum has additional angular regularity.

KW - Bessel function

KW - Linear adjoint restriction estimate

KW - Local restriction estimate

KW - Local smoothing

KW - Spherical harmonics

UR - http://www.scopus.com/inward/record.url?scp=85061308219&partnerID=8YFLogxK

U2 - 10.1007/s00209-019-02251-7

DO - 10.1007/s00209-019-02251-7

M3 - Article

AN - SCOPUS:85061308219

SN - 0025-5874

VL - 292

SP - 427

EP - 451

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 1-2

ER -

Linear adjoint restriction estimates for paraboloid

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Keywords

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