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

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

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].

Original language	English
Pages (from-to)	2752-2775
Number of pages	24
Journal	Journal of Functional Analysis
Volume	271
Issue number	10
DOIs	https://doi.org/10.1016/j.jfa.2016.04.015
Publication status	Published - 15 Nov 2016
Externally published	Yes

Keywords

Bilinear estimates
Eigenfunctions
Kakeya–Nikodym averages

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10.1016/j.jfa.2016.04.015

Cite this

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title = "Bilinear Kakeya–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–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–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",

volume = "271",

pages = "2752--2775",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "10",

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TY - JOUR

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

Abstract

Keywords

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