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

^*此作品的通讯作者

数学学院

科研成果: 期刊稿件 › 文章 › 同行评审

5 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	427-451
页数	25
期刊	Mathematische Zeitschrift
卷	292
期	1-2
DOI	https://doi.org/10.1007/s00209-019-02251-7
出版状态	已出版 - 1 6月 2019

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Miao, C., Zhang, J., & Zheng, J. (2019). Linear adjoint restriction estimates for paraboloid. Mathematische Zeitschrift, 292(1-2), 427-451. https://doi.org/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",

note = "Publisher Copyright: {\textcopyright} 2019, The Author(s).",

year = "2019",

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doi = "10.1007/s00209-019-02251-7",

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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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