Bilinear Kakeya–Nikodym averages of eigenfunctions on compact Riemannian surfaces

Changxing Miao; Christopher D. Sogge; Yakun Xi; Jianwei Yang

doi:10.1016/j.jfa.2016.04.015

Bilinear Kakeya–Nikodym averages of eigenfunctions on compact Riemannian surfaces

Changxing Miao
, Christopher D. Sogge
, Yakun Xi^*
, Jianwei Yang

^*此作品的通讯作者

IAPCM
Johns Hopkins University
Université Paris 13
Peking University

科研成果: 期刊稿件 › 文章 › 同行评审

3 引用（Scopus）

摘要

We obtain an improvement of the bilinear estimates of Burq, Gérard and Tzvetkov [6] in the spirit of the refined Kakeya–Nikodym estimates [2] of Blair and the second author. We do this by using microlocal techniques and a bilinear version of Hörmander's oscillatory integral theorem in [7].

源语言	英语
页（从-至）	2752-2775
页数	24
期刊	Journal of Functional Analysis
卷	271
期	10
DOI	https://doi.org/10.1016/j.jfa.2016.04.015
出版状态	已出版 - 15 11月 2016
已对外发布	是

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title = "Bilinear Kakeya{\textendash}Nikodym averages of eigenfunctions on compact Riemannian surfaces",

abstract = "We obtain an improvement of the bilinear estimates of Burq, G{\'e}rard and Tzvetkov [6] in the spirit of the refined Kakeya{\textendash}Nikodym estimates [2] of Blair and the second author. We do this by using microlocal techniques and a bilinear version of H{\"o}rmander's oscillatory integral theorem in [7].",

keywords = "Bilinear estimates, Eigenfunctions, Kakeya{\textendash}Nikodym averages",

author = "Changxing Miao and Sogge, \{Christopher D.\} and Yakun Xi and Jianwei Yang",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

year = "2016",

month = nov,

day = "15",

doi = "10.1016/j.jfa.2016.04.015",

language = "English",

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T1 - Bilinear Kakeya–Nikodym averages of eigenfunctions on compact Riemannian surfaces

AU - Miao, Changxing

AU - Sogge, Christopher D.

AU - Xi, Yakun

AU - Yang, Jianwei

PY - 2016/11/15

Y1 - 2016/11/15

N2 - We obtain an improvement of the bilinear estimates of Burq, Gérard and Tzvetkov [6] in the spirit of the refined Kakeya–Nikodym estimates [2] of Blair and the second author. We do this by using microlocal techniques and a bilinear version of Hörmander's oscillatory integral theorem in [7].

AB - We obtain an improvement of the bilinear estimates of Burq, Gérard and Tzvetkov [6] in the spirit of the refined Kakeya–Nikodym estimates [2] of Blair and the second author. We do this by using microlocal techniques and a bilinear version of Hörmander's oscillatory integral theorem in [7].

KW - Bilinear estimates

KW - Eigenfunctions

KW - Kakeya–Nikodym averages

UR - https://www.scopus.com/pages/publications/84963979646

U2 - 10.1016/j.jfa.2016.04.015

DO - 10.1016/j.jfa.2016.04.015

M3 - Article

AN - SCOPUS:84963979646

SN - 0022-1236

VL - 271

SP - 2752

EP - 2775

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 10

ER -

Bilinear Kakeya–Nikodym averages of eigenfunctions on compact Riemannian surfaces

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