• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Conjectures associated with Brascamp-Lieb type inequalities

Research Project

Project/Area Number 16H05995
Research Category

Grant-in-Aid for Young Scientists (A)

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionSaitama University

Principal Investigator

BEZ Neal  埼玉大学, 理工学研究科, 准教授 (30729843)

Research Collaborator BENNETT Jonathan  
COWLING Michael  
CUNANAN Jayson  
FLOCK Taryn  
GUTIERREZ Susana  
ILIOPOULOU Marina  
JEAVONS Chris  
LEE Sanghyuk  
NAKAMURA Shohei  
OZAWA Tohru  
SAWANO Yoshihiro  
SUGIMOTO Mitsuru  
Project Period (FY) 2016-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥13,130,000 (Direct Cost: ¥10,100,000、Indirect Cost: ¥3,030,000)
Fiscal Year 2018: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2017: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2016: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
KeywordsBrascamp-Lieb不等式 / 安定性 / Brascamp-Lieb inequality / Stability / 実解析 / 調和解析 / Schrodinger equation / Transport equation / Trace estimates
Outline of Final Research Achievements

A key outcome of this research project was the successful complete verification of the nonlinear Brascamp-Lieb (BL) conjecture. This was one of the main goals of the initial research proposal and has been achieved through a series of papers. The first step was to establish local boundedness of the BL constant in the standard version of the BL inequality and use this to prove the nonlinear BL conjecture for input functions with arbitrarily small Sobolev regularity. As a further application of this stability result, we advanced the theory of the multilinear Fourier restriction problem. Next, we showed continuity of the BL constant and this result was used in our recent complete resolution of the nonlinear BL conjecture. Additionally, this research project has produced various new developments on related theory, including estimates for the kinetic transport equation.

Academic Significance and Societal Importance of the Research Achievements

非線形ブラスカンプ・リーブ予想を証明した事により、抽象調和解析や偏微分方程式への応用を行った。例えば、リー群に関する局所的なヤングの畳み込み不等式に対する最良定数を求めた。更に、ザハロフ方程式系の理論における幾何的な不等式を示す事にも成功した。このように本研究の成果は、将来的にも多分野で応用される事が期待される。

調和解析および幾何解析の研究交流を更に推進するために、4日間の国際的な研究集会を東京ステーションカレッジ・埼玉大学サテライトキャンパスで開催した。

Report

(4 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Annual Research Report
  • 2016 Annual Research Report
  • Research Products

    (28 results)

All 2018 2017 2016

All Journal Article (8 results) (of which Int'l Joint Research: 8 results,  Peer Reviewed: 8 results,  Open Access: 2 results,  Acknowledgement Compliant: 1 results) Presentation (19 results) (of which Int'l Joint Research: 14 results,  Invited: 18 results) Funded Workshop (1 results)

  • [Journal Article] Stability of the Brascamp-Lieb constant and applications2018

    • Author(s)
      Bennett Jonathan、Bez Neal、Flock Taryn C.、Lee Sanghyuk
    • Journal Title

      American Journal of Mathematics

      Volume: 140 Issue: 2 Pages: 543-569

    • DOI

      10.1353/ajm.2018.0013

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Estimates for the kinetic transport equation in hyperbolic Sobolev spaces2018

    • Author(s)
      Bennett Jonathan、Bez Neal、Gutierrez Susana、Lee Sanghyuk
    • Journal Title

      Journal de Mathematiques Pures et Appliquees

      Volume: 114 Pages: 1-28

    • DOI

      10.1016/j.matpur.2018.03.007

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Stability of Trace Theorems on the Sphere2018

    • Author(s)
      Neal Bez, Chris Jeavons, Tohru Ozawa, Mitsuru Sugimoto
    • Journal Title

      The Journal of Geometric Analysis

      Volume: 28 Issue: 2 Pages: 1456-1476

    • DOI

      10.1007/s12220-017-9870-8

    • NAID

      120006496423

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Smoothing Estimates for the Kinetic Transport Equation at the Critical Regularity2018

    • Author(s)
      Bez Neal, Cunanan Jayson, Lee Sanghyuk
    • Journal Title

      SIAM Journal on Mathematical Analysis

      Volume: 50 Issue: 2 Pages: 2280-2294

    • DOI

      10.1137/17m1148852

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A sharp k-plane Strichartz inequality for the Schrodinger equation2018

    • Author(s)
      Jonathan Bennett, Neal Bez, Taryn Flock, Susana Gutierrez, Marina Iliopoulou
    • Journal Title

      Transactions of the American Mathematical Society

      Volume: - Issue: 8 Pages: 5617-5633

    • DOI

      10.1090/tran/7309

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Generating monotone quantities for the heat equation2018

    • Author(s)
      Jonathan Bennett, Neal Bez
    • Journal Title

      Journal fur die reine und angewandte Mathematik

      Volume: - Issue: 756 Pages: 37-63

    • DOI

      10.1515/crelle-2017-0025

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Sharpness of the Brascamp--Lieb inequality in Lorentz spaces2017

    • Author(s)
      Bez Neal、Lee Sanghyuk、Nakamura Shohei、Sawano Yoshihiro
    • Journal Title

      Electron. Res. Announc. Math. Sci.

      Volume: 24 Issue: 0 Pages: 53-63

    • DOI

      10.3934/era.2017.24.006

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Behaviour of the Brascamp-Lieb constant2017

    • Author(s)
      Jonathan Bennett, Neal Bez, Michael Cowling, Taryn Flock
    • Journal Title

      Bulletin of the London Mathematical Society

      Volume: - Issue: 3 Pages: 512-518

    • DOI

      10.1112/blms.12049

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] Smoothing estimates for the kinetic transport equation at the critical regularity2018

    • Author(s)
      Neal Bez
    • Organizer
      保存則をもつ偏微分方程式の解の正則性,特異性および漸近挙動の研究、RIMS共同研究
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] On the kinetic transport equation2018

    • Author(s)
      Neal Bez
    • Organizer
      調和解析と非線形偏微分方程式、RIMS共同研究
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Strichartz estimates for orthonormal systems of initial data2018

    • Author(s)
      Neal Bez
    • Organizer
      International Workshop on Fundamental Problems in Mathematical and Theoretical Physics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Mixed-norm estimates for multipliers associated with some hypersurfaces2018

    • Author(s)
      Neal Bez
    • Organizer
      Harmonic Analysis and PDE Workshop
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Geometric estimates arising in the analysis of Zakharov systems2018

    • Author(s)
      Neal Bez
    • Organizer
      2018日本数学会秋季総合分科会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Strichartz estimates for orthonormal systems of initial data2018

    • Author(s)
      Neal Bez
    • Organizer
      16th Linear and Nonlinear Waves Conference
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Harmonic analysis techniques and orthonormal Strichartz estimates2018

    • Author(s)
      Neal Bez
    • Organizer
      Strobl18 Harmonic Analysis and Applications
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Smoothing estimates for velocity averages2018

    • Author(s)
      Neal Bez
    • Organizer
      九州関数方程式セミナー
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Multilinear restriction and Kakeya estimates2017

    • Author(s)
      Neal Bez
    • Organizer
      Yonsei University Analysis Seminar
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the kinetic transport equation2017

    • Author(s)
      Neal Bez
    • Organizer
      Harmonic Analysis and its Interactions: in Honour of Tony Carbery
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Strichartz estimates for orthonormal systems of initial data2017

    • Author(s)
      Neal Bez
    • Organizer
      Nonlinear Partial Differential Equations for Future Applications: Hyperbolic and Dispersive PDE
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Multilinear inequalities in harmonic and geometric analysis2017

    • Author(s)
      Neal Bez
    • Organizer
      Topics in Harmonic Analysis: Intensive Lecture Series
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Stability of the Brascamp-Lieb inequality2017

    • Author(s)
      Neal Bez
    • Organizer
      Analysis Seminar
    • Place of Presentation
      University of Edinburgh (United Kingdom)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Smoothing estimates for the kinetic transport equation via the cone multiplier2017

    • Author(s)
      Neal Bez
    • Organizer
      Harmonic Analysis Workshop
    • Place of Presentation
      金沢大学 (石川県金沢市)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Smoothing estimates for velocity averages via the cone multiplier2017

    • Author(s)
      Neal Bez
    • Organizer
      Harmonic Analysis and Applications
    • Place of Presentation
      Seoul National University (South Korea)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Stability of the Brascamp-Lieb constant and applications2016

    • Author(s)
      Neal Bez
    • Organizer
      International Conference for the 70th Anniversary of the Korean Mathematical Society
    • Place of Presentation
      Seoul National University (South Korea)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Estimates for the kinetic transport equation in hyperbolic Sobolev spaces2016

    • Author(s)
      Neal Bez
    • Organizer
      Analysis Seminar
    • Place of Presentation
      Seoul National University (South Korea)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Stability of the Brascamp-Lieb constant and applications2016

    • Author(s)
      Neal Bez
    • Organizer
      4th East Asian Conference in Harmonic Analysis and Applications
    • Place of Presentation
      Yonsei University (South Korea)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Strichartz estimates for the kinetic and Schrodinger equations2016

    • Author(s)
      Neal Bez
    • Organizer
      Analysis Seminar
    • Place of Presentation
      Seoul National University (South Korea)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Funded Workshop] Interactions Between Harmonic And Geometric Analysis2016

    • Place of Presentation
      埼玉大学・東京ステーションカレッジ・埼玉大学サテライトキャンパス (東京都千代田区)
    • Year and Date
      2016-11-28
    • Related Report
      2016 Annual Research Report

URL: 

Published: 2016-04-21   Modified: 2020-03-30  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi