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BEZ　Neal Richard
Mathematics, Electronics and Informatics DivisionProfessor
Mathematics

Researcher information

■ Degree
  • PhD, University of Edinburgh
  • Masters, University of Oxford
■ Research Keyword
  • Harmonic Analysis
  • Geometric Analysis
  • Partial Differential Equations
■ Field Of Study
  • Natural sciences, Mathematical analysis
■ Award
  • Mar. 2022, Spring Prize, Mathematical Society of Japan
  • Apr. 2020, Science and Technology Young Scientists' Prize, MEXT
  • Mar. 2018, 2018 JMSJ Outstanding Paper Prize
    Jonathan Bennett;Neal Bez;Chris Jeavons;Nikolaos Pattakos
  • Sep. 2014, Takebe Katahiro Prize, Mathematical Society of Japan

Performance information

■ Paper
  • A note on ubiquity of geometric Brascamp–Lieb data
    Neal Bez; Anthony Gauvan; Hiroshi Tsuji
    Bulletin of the London Mathematical Society, Volume：57, Number：1, First page：302, Last page：314, Dec. 2024, [Reviewed]
    Abstract

    Relying substantially on work of Garg, Gurvits, Oliveira and Wigderson, it is shown that geometric Brascamp–Lieb data are, in a certain sense, dense in the space of feasible Brascamp–Lieb data. This addresses a question raised by Bennett and Tao in their recent work on the adjoint Brascamp–Lieb inequality.
    Wiley, Scientific journal
    DOI：https://doi.org/10.1112/blms.13198
    DOI ID：10.1112/blms.13198, ISSN：0024-6093, eISSN：1469-2120
  • Boundary Strichartz estimates and pointwise convergence for orthonormal systems
    Neal Bez; Shinya Kinoshita; Shobu Shiraki
    Transactions of the London Mathematical Society, Volume：11, Number：1, Dec. 2024, [Reviewed]
    Abstract

    We consider maximal estimates associated with fermionic systems. Firstly, we establish maximal estimates with respect to the spatial variable. These estimates are certain boundary cases of the many‐body Strichartz estimates pioneered by Frank, Lewin, Lieb and Seiringer. We also prove new maximal‐in‐time estimates, thereby significantly extending work of Lee, Nakamura and the first author on Carleson's pointwise convergence problem for fermionic systems.
    Wiley, Scientific journal
    DOI：https://doi.org/10.1112/tlm3.70002
    DOI ID：10.1112/tlm3.70002, ISSN：2052-4986, eISSN：2052-4986
  • Stability of hypercontractivity, the logarithmic Sobolev inequality, and Talagrand's cost inequality　　　　　　　　　　　　　　　
    Neal Bez; Shohei Nakamura; Hiroshi Tsuji
    Journal of Functional Analysis, Volume：285, Number：10, First page：110121, Last page：110121, Nov. 2023, [Reviewed]
    Elsevier BV, Scientific journal
    DOI：https://doi.org/10.1016/j.jfa.2023.110121
    DOI ID：10.1016/j.jfa.2023.110121, ISSN：0022-1236
  • Revisiting the Rellich inequality
    Neal Bez; Shuji Machihara; Tohru Ozawa
    Mathematische Zeitschrift, Volume：303, Number：2, Jan. 2023, [Reviewed]
    Springer Science and Business Media LLC, Scientific journal
    DOI：https://doi.org/10.1007/s00209-022-03203-4
    DOI ID：10.1007/s00209-022-03203-4, ISSN：0025-5874, eISSN：1432-1823
  • Higher order transversality in harmonic analysis　　　　　　　　　　　　　　　
    Jonathan Bennett; Neal Bez
    RIMS Kôkyûroku Bessatsu, Volume：B88, First page：75, Last page：103, 2021, [Reviewed]
  • Strichartz estimates for orthonormal families of initial data and weighted oscillatory integral estimates
    Neal Bez; Sanghyuk Lee; Shohei Nakamura
    Forum of Mathematics, Sigma, Volume：9, 2021, [Reviewed]
    Abstract
    We establish new Strichartz estimates for orthonormal families of initial data in the case of the wave, Klein–Gordon and fractional Schrödinger equations. Our estimates extend those of Frank–Sabin in the case of the wave and Klein–Gordon equations, and generalize work of Frank et al. and Frank–Sabin for the Schrödinger equation. Due to a certain technical barrier, except for the classical Schrödinger equation, the Strichartz estimates for orthonormal families of initial data have not previously been established up to the sharp summability exponents in the full range of admissible pairs. We obtain the optimal estimates in various notable cases and improve the previous results.


    The main novelty of this paper is our derivation and use of estimates for weighted oscillatory integrals, which we combine with an approach due to Frank and Sabin. Our weighted oscillatory integral estimates are, in a certain sense, rather delicate endpoint versions of known dispersive estimates with power-type weights of the form


    $|\xi |^{-\lambda }$

     or


    $(1 + |\xi |^2)^{-\lambda /2}$

    , where


    $\lambda \in \mathbb {R}$

    . We achieve optimal decay rates by considering such weights with appropriate


    $\lambda \in \mathbb {C}$

    . For the wave and Klein–Gordon equations, our weighted oscillatory integral estimates are new. For the fractional Schrödinger equation, our results overlap with prior work of Kenig–Ponce–Vega in a certain regime. Our contribution to the theory of weighted oscillatory integrals has also been influenced by earlier work of Carbery–Ziesler, Cowling et al., and Sogge–Stein.


    Finally, we provide some applications of our new Strichartz estimates for orthonormal families of data to the theory of infinite systems of Hartree type, weighted velocity averaging lemmas for kinetic transport equations, and refined Strichartz estimates for data in Besov spaces.
    Cambridge University Press (CUP), Scientific journal
    DOI：https://doi.org/10.1017/fms.2020.64
    DOI ID：10.1017/fms.2020.64, eISSN：2050-5094
  • On the nonlinear Brascamp-Lieb inequality　　　　　　　　　　　　　　　
    Jonathan Bennett; Neal Bez; Stefan Buschenhenke; Michael Cowling; Taryn Flock
    Duke Mathematical Journal, Volume：169, First page：3291, Last page：3338, 2020, [Reviewed]
  • Maximal estimates for the Schrodinger equation with orthonormal initial data
    Neal Bez; Sanghyuk Lee; Shohei Nakamura
    Selecta Mathematica, Volume：26, Number：52, 2020, [Reviewed]
    Springer Science and Business Media LLC, Scientific journal
    DOI：https://doi.org/10.1007/s00029-020-00582-6
    DOI ID：10.1007/s00029-020-00582-6, ISSN：1022-1824, eISSN：1420-9020
  • A supersolutions perspective on hypercontractivity　　　　　　　　　　　　　　　
    Yosuke Aoki; Jonathan Bennett; Neal Bez; Shuji Machihara; Kosuke Matsuura; Shobu Shiraki
    Annali di Matematica Pura ed Applicata, Volume：199, First page：2105, Last page：2116, 2020, [Reviewed]
  • Inhomogeneous Strichartz estimates in some critical cases　　　　　　　　　　　　　　　
    Neal Bez; Jayson Cunanan; Sanghyuk Lee
    Proceedings of the American Mathematical Society, Volume：148, First page：639, Last page：652, 2020, [Reviewed]
  • Hardy type inequalities with spherical derivatives　　　　　　　　　　　　　　　
    Neal Bez; Shuji Machihara; Tohru Ozawa
    SN Partial Differential Equations and Applications, Volume：1, Number：5, 2020, [Reviewed]
  • On the Strichartz estimates for orthonormal systems of initial data with regularity　　　　　　　　　　　　　　　
    Neal Bez; Younghun Hong; Sanghyuk Lee; Shohei Nakamura; Yoshihiro Sawano
    Advances in Mathematics, Volume：354, Number：106736, First page：106736, Last page：106736, 2019, [Reviewed]
    Elsevier BV, Scientific journal
    DOI：https://doi.org/10.1016/j.aim.2019.106736
    DOI ID：10.1016/j.aim.2019.106736, ISSN：0001-8708
  • Smoothing estimates for velocity averages with radial data　　　　　　　　　　　　　　　
    Neal Bez; Jayson Cunanan
    RIMS Kokyuroku Bessatsu, Volume：B74, First page：33, Last page：46, 2019, [Reviewed]
  • Remarks on the Mizohata-Takeuchi conjecture and related problems　　　　　　　　　　　　　　　
    Neal Bez; Mitsuru Sugimoto
    Advanced Studies in Pure Mathematics, Volume：81, First page：1, Last page：12, 2019, [Reviewed]
  • Generating monotone quantities for the heat equation　　　　　　　　　　　　　　　
    Jonathan Bennett; Neal Bez
    Journal fur die Reine und Angewandte Mathematik, Volume：756, First page：37, Last page：63, 2019, [Reviewed]
  • Estimates for the kinetic transport equation in hyperbolic Sobolev spaces　　　　　　　　　　　　　　　
    Jonathan Bennett; Neal Bez; Susana Gutiérrez; Sanghyuk Lee
    Journal des Mathematiques Pures et Appliquees, Volume：114, First page：1, Last page：28, Jun. 2018, [Reviewed]
    Elsevier Masson SAS, English, Scientific journal
    DOI：https://doi.org/10.1016/j.matpur.2018.03.007
    DOI ID：10.1016/j.matpur.2018.03.007, ISSN：0021-7824, SCOPUS ID：85045703051
  • A sharp k-plane strichartz inequality for the schrödinger equation　　　　　　　　　　　　　　　
    Jonathan Bennett; Neal Bez; Taryn C. Flock; Susana Gutiérrez; Marina Iliopoulou
    Transactions of the American Mathematical Society, Volume：370, Number：8, First page：5617, Last page：5633, 2018, [Reviewed]
    American Mathematical Society, English, Scientific journal
    DOI：https://doi.org/10.1090/tran/7309
    DOI ID：10.1090/tran/7309, ISSN：0002-9947, SCOPUS ID：85047105131
  • Stability of the Brascamp-Lieb constant and applications　　　　　　　　　　　　　　　
    J. Bennett; N. Bez; T. Flock; S. Lee
    American Journal of Mathematics, Volume：140, First page：543, Last page：569, 2018, [Reviewed]
  • Stability of trace theorems on the sphere　　　　　　　　　　　　　　　
    N. Bez; C. Jeavons; T. Ozawa; M. Sugimoto
    Journal of Geometric Analysis, Volume：28, First page：1456, Last page：1476, 2018, [Reviewed]
  • Smoothing estimates for the kinetic transport equation at the critical regularity　　　　　　　　　　　　　　　
    Neal Bez; Jayson Cunanan; Sanghyuk Lee
    SIAM Journal on Mathematical Analysis, Volume：50, Number：2, First page：2280, Last page：2294, 2018, [Reviewed]
    Society for Industrial and Applied Mathematics Publications, English, Scientific journal
    DOI：https://doi.org/10.1137/17M1148852
    DOI ID：10.1137/17M1148852, ISSN：1095-7154, SCOPUS ID：85047342233
  • Behaviour of the Brascamp-Lieb constant　　　　　　　　　　　　　　　
    Jonathan Bennett; Neal Bez; Michael G. Cowling; Taryn C. Flock
    BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, Volume：49, Number：3, First page：512, Last page：518, Jun. 2017, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.1112/blms.12049
    DOI ID：10.1112/blms.12049, ISSN：0024-6093, eISSN：1469-2120, Web of Science ID：WOS:000402144800014
  • On sharp bilinear Strichartz estimates of Ozawa-Tsutsumi type　　　　　　　　　　　　　　　
    Jonathan Bennett; Neal Bez; Chris Jeavons; Nikolaos Pattakos
    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, Volume：69, Number：2, First page：459, Last page：476, Apr. 2017, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.2969/jmsj/06920459
    DOI ID：10.2969/jmsj/06920459, ISSN：0025-5645, Web of Science ID：WOS:000401401300001
  • A conjecture regarding optimal Strichartz estimates for the wave equation　　　　　　　　　　　　　　　
    N. Bez; C. Jeavons; T. Ozawa; H. Saito
    Trends in Mathematics (New Trends in Analysis and Interdisciplinary Applications), 2017, [Reviewed]
  • Optimal constants and extremisers for some smoothing estimates　　　　　　　　　　　　　　　
    N. Bez; M. Sugimoto
    Journal d'Analyse Mathematique, Volume：131, First page：159, Last page：187, 2017, [Reviewed]
  • Sharpness of the brascamp-lieb inequality in lorentz spaces　　　　　　　　　　　　　　　
    Neal Bez; Sanghyuk Lee; Shohei Nakamura; Yoshihiro Sawano
    Electronic Research Announcements in Mathematical Sciences, Volume：24, First page：53, Last page：63, 2017, [Reviewed]
    American Mathematical Society, English, Scientific journal
    DOI：https://doi.org/10.3934/era.2017.24.006
    Scopus：https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85020907812&origin=inward
    Scopus Citedby：https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85020907812&origin=inward
    DOI ID：10.3934/era.2017.24.006, ISSN：1935-9179, SCOPUS ID：85020907812
  • SOME SHARP BILINEAR SPACE-TIME ESTIMATES FOR THE WAVE EQUATION　　　　　　　　　　　　　　　
    Neal Bez; Chris Jeavons; Tohru Ozawa
    MATHEMATIKA, Volume：62, Number：3, First page：719, Last page：737, 2016, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.1112/S0025579316000012
    DOI ID：10.1112/S0025579316000012, ISSN：0025-5793, eISSN：2041-7942, Web of Science ID：WOS:000375948100005
  • Extremisers for the trace theorem on the sphere　　　　　　　　　　　　　　　
    Neal Bez; Shuji Machihara; Mitsuru Sugimoto
    MATHEMATICAL RESEARCH LETTERS, Volume：23, Number：3, First page：633, Last page：647, 2016, [Reviewed]
    English, Scientific journal
    ISSN：1073-2780, eISSN：1945-001X, Web of Science ID：WOS:000388457200003
  • A survey on optimal smoothing estimates and trace theorems　　　　　　　　　　　　　　　
    N. Bez; M. Sugimoto
    Advances in Mathematics (China), Volume：45, First page：801, Last page：816, 2016, [Reviewed]
  • Applications of the Funk-Hecke theorem to smoothing and trace estimates　　　　　　　　　　　　　　　
    Neal Bez; Hiroki Saito; Mitsuru Sugimoto
    ADVANCES IN MATHEMATICS, Volume：285, First page：1767, Last page：1795, Nov. 2015, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.1016/j.aim.2015.08.025
    DOI ID：10.1016/j.aim.2015.08.025, ISSN：0001-8708, eISSN：1090-2082, Web of Science ID：WOS:000376417800048
  • Optimal Forward and Reverse Estimates of Morawetz and Kato-Yajima Type with Angular Smoothing Index　　　　　　　　　　　　　　　
    Neal Bez; Mitsuru Sugimoto
    JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, Volume：21, Number：2, First page：318, Last page：341, Apr. 2015, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.1007/s00041-014-9371-0
    DOI ID：10.1007/s00041-014-9371-0, ISSN：1069-5869, eISSN：1531-5851, Web of Science ID：WOS:000351174800004
  • Some Recent Progress on Sharp Kato-type Smoothing Estimates　　　　　　　　　　　　　　　
    Neal Bez; Mitsuru Sugimoto
    COMPLEX ANALYSIS AND DYNAMICAL SYSTEMS VI, PT 1: PDE, DIFFERENTIAL GEOMETRY, RADON TRANSFORM, Volume：653, First page：41, Last page：50, 2015, [Reviewed]
    English, International conference proceedings
    DOI：https://doi.org/10.1090/conm/653/13177
    DOI ID：10.1090/conm/653/13177, ISSN：0271-4132, Web of Science ID：WOS:000371648700004
  • Sharp sobolev-strichartz estimates for the free Schrödinger propagator　　　　　　　　　　　　　　　
    Neal Bez; Chris Jeavons; Nikolaos Pattakos
    Trends in Mathematics, Volume：2, First page：281, Last page：288, 2015, [Reviewed]
    Springer International Publishing, English, International conference proceedings
    DOI：https://doi.org/10.1007/978-3-319-12577-0-33
    DOI ID：10.1007/978-3-319-12577-0-33, ISSN：2297-024X, SCOPUS ID：84959159490
  • A SHARP SOBOLEV-STRICHARTZ ESTIMATE FOR THE WAVE EQUATION　　　　　　　　　　　　　　　
    Neal Bez; Chris Jeavons
    ELECTRONIC RESEARCH ANNOUNCEMENTS IN MATHEMATICAL SCIENCES, Volume：22, First page：46, Last page：54, 2015, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.3934/era.2015.22.46
    DOI ID：10.3934/era.2015.22.46, ISSN：1935-9179, Web of Science ID：WOS:000361819700005
  • Flow Monotonicity and Strichartz Inequalities　　　　　　　　　　　　　　　
    Jonathan Bennett; Neal Bez; Marina Iliopoulou
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, Number：19, First page：9415, Last page：9437, 2015, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.1093/imrn/rnu230
    DOI ID：10.1093/imrn/rnu230, ISSN：1073-7928, eISSN：1687-0247, Web of Science ID：WOS:000366499400008
  • Optimal constant for a smoothing estimate of critical index　　　　　　　　　　　　　　　
    N. Bez; M. Sugimoto
    Trends in Mathematics (Fourier Analysis), First page：1, Last page：7, 2014, [Reviewed]
  • On the Strichartz Estimates for the Kinetic Transport Equation　　　　　　　　　　　　　　　
    Jonathan Bennett; Neal Bez; Susana Gutierrez; Sanghyuk Lee
    COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, Volume：39, Number：10, First page：1821, Last page：1826, 2014, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.1080/03605302.2013.850880
    DOI ID：10.1080/03605302.2013.850880, ISSN：0360-5302, eISSN：1532-4133, Web of Science ID：WOS:000341003700001
  • A note on magnitude bounds for the mask coefficients of the interpolatory Dubuc-Deslauriers subdivision scheme　　　　　　　　　　　　　　　
    H. E. Bez; N. Bez
    LMS JOURNAL OF COMPUTATION AND MATHEMATICS, Volume：17, Number：1, First page：226, Last page：232, 2014, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.1112/S1461157013000363
    DOI ID：10.1112/S1461157013000363, ISSN：1461-1570, Web of Science ID：WOS:000349291700013
  • New minimal bounds for the derivatives of rational Bezier paths and rational rectangular Bezier surfaces　　　　　　　　　　　　　　　
    H. E. Bez; N. Bez
    APPLIED MATHEMATICS AND COMPUTATION, Volume：225, First page：475, Last page：479, Dec. 2013, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.1016/j.amc.2013.09.039
    DOI ID：10.1016/j.amc.2013.09.039, ISSN：0096-3003, eISSN：1873-5649, Web of Science ID：WOS:000327765600041
  • Global Nonlinear Brascamp-Lieb Inequalities　　　　　　　　　　　　　　　
    Jonathan Bennett; Neal Bez; Susana Gutierrez
    JOURNAL OF GEOMETRIC ANALYSIS, Volume：23, Number：4, First page：1806, Last page：1817, Oct. 2013, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.1007/s12220-012-9307-3
    DOI ID：10.1007/s12220-012-9307-3, ISSN：1050-6926, Web of Science ID：WOS:000325065700009
  • On derivative bounds for the rational quadratic Bezier paths　　　　　　　　　　　　　　　
    H. E. Bez; N. Bez
    COMPUTER AIDED GEOMETRIC DESIGN, Volume：30, Number：2, First page：254, Last page：261, Feb. 2013, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.1016/j.cagd.2012.12.003
    DOI ID：10.1016/j.cagd.2012.12.003, ISSN：0167-8396, Web of Science ID：WOS:000316037900006
  • Transversal multilinear Radon-like transforms: local and global estimates　　　　　　　　　　　　　　　
    Jonathan Bennett; Neal Bez; Susana Gutierrez
    REVISTA MATEMATICA IBEROAMERICANA, Volume：29, Number：3, First page：765, Last page：788, 2013, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.4171/RMI/739
    DOI ID：10.4171/RMI/739, ISSN：0213-2230, Web of Science ID：WOS:000326990500002
  • A sharp Strichartz estimate for the wave equation with data in the energy space　　　　　　　　　　　　　　　
    Neal Bez; Keith M. Rogers
    JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, Volume：15, Number：3, First page：805, Last page：823, 2013, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.4171/JEMS/377
    DOI ID：10.4171/JEMS/377, ISSN：1435-9855, Web of Science ID：WOS:000317564700005
  • A majorant problem for the periodic Schrodinger group　　　　　　　　　　　　　　　
    J. Bennett; N. Bez
    RIMS Kokyuroku Bessatsu, Volume：B33, First page：1, Last page：10, 2012, [Reviewed]
  • Some nonlinear Brascamp-Lieb inequalities and applications to harmonic analysis　　　　　　　　　　　　　　　
    Jonathan Bennett; Neal Bez
    JOURNAL OF FUNCTIONAL ANALYSIS, Volume：259, Number：10, First page：2520, Last page：2556, Nov. 2010, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.1016/j.jfa.2010.07.015
    DOI ID：10.1016/j.jfa.2010.07.015, ISSN：0022-1236, Web of Science ID：WOS:000281532200002
  • Heat-flow monotonicity related to the Hausdorff-Young inequality　　　　　　　　　　　　　　　
    Jonathan Bennett; Neal Bez; Anthony Carbery
    BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, Volume：41, First page：971, Last page：979, Dec. 2009, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.1112/blms/bdp073
    DOI ID：10.1112/blms/bdp073, ISSN：0024-6093, Web of Science ID：WOS:000272924700002
  • MAXIMAL OPERATORS AND HILBERT TRANSFORMS ALONG FLAT CURVES NEAR L-1　　　　　　　　　　　　　　　
    Neal Bez
    JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, Volume：87, Number：3, First page：311, Last page：323, Dec. 2009, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.1017/S1446788709000111
    DOI ID：10.1017/S1446788709000111, ISSN：1446-7887, Web of Science ID：WOS:000273957500002
  • Closure Properties of Solutions to Heat Inequalities　　　　　　　　　　　　　　　
    Jonathan Bennett; Neal Bez
    JOURNAL OF GEOMETRIC ANALYSIS, Volume：19, Number：3, First page：584, Last page：600, Jul. 2009, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.1007/s12220-009-9070-2
    DOI ID：10.1007/s12220-009-9070-2, ISSN：1050-6926, Web of Science ID：WOS:000265214800005
  • Heat-flow monotonicity underlying some sharp inequalities in geometric and harmonic analysis　　　　　　　　　　　　　　　
    N. Bez
    RIMS Kokyuroku Bessatsu, Volume：B14, First page：1, Last page：16, 2009, [Reviewed]
    Kyoto University, English
    ISSN：1881-6193, CiNii Articles ID：110007480919, CiNii Books ID：AA12196120
  • HEAT-FLOW MONOTONICITY OF STRICHARTZ NORMS　　　　　　　　　　　　　　　
    Jonathan Bennett; Neal Bez; Anthony Carbery; Dirk Hundertmark
    ANALYSIS & PDE, Volume：2, Number：2, First page：147, Last page：158, 2009, [Reviewed]
    English, Scientific journal
    ISSN：1948-206X, Web of Science ID：WOS:000281883500002
  • Maximal Operators along Piecewise Linear Curves near L-1　　　　　　　　　　　　　　　
    Neal Bez
    INDIANA UNIVERSITY MATHEMATICS JOURNAL, Volume：58, Number：4, First page：1639, Last page：1657, 2009, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.1512/iumj.2009.58.3606
    DOI ID：10.1512/iumj.2009.58.3606, ISSN：0022-2518, Web of Science ID：WOS:000269448000006
  • Mixed-norm estimates for a class of nonisotropic directional maximal operators and Hilbert transforms　　　　　　　　　　　　　　　
    Neal Bez
    JOURNAL OF FUNCTIONAL ANALYSIS, Volume：255, Number：12, First page：3281, Last page：3302, Dec. 2008, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.1016/j.jfa.2008.07.026
    DOI ID：10.1016/j.jfa.2008.07.026, ISSN：0022-1236, Web of Science ID：WOS:000261578900003
  • L-p-boundedness for the Hilbert transform and maximal operator along a class of nonconvex curves　　　　　　　　　　　　　　　
    Neal Bez
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, Volume：135, Number：1, First page：151, Last page：161, 2007, [Reviewed]
    English, Scientific journal
    DOI：https://doi.org/10.1090/S0002-9939-06-08603-5
    DOI ID：10.1090/S0002-9939-06-08603-5, ISSN：0002-9939, Web of Science ID：WOS:000240542200020
■ MISC
  • 滑らかさを加味した直交ストリッカーツ評価 (関数空間の一般化とその周辺)　　　　　　　　　　　　　　　
    BEZ NEAL; HONG YOUNGHUN; LEE SANGHYUK; 中村 昌平; 澤野 嘉宏
    Number：2143, First page：173, Last page：184, Dec. 2019
    直交ストリッカーツ評価と呼ばれる新しい評価を示す. 最初に, FrankとSabinによる関数の滑らかさを加味しない直交ストリッカーツ評価[5]を示し, 後で我々による関数の滑らかさを加味した直交ストリッカーツ評価のひとつの場合の証明する. この結果は我々の論文[2]として出版されている.
    Japanese
    ISSN：1880-2818, CiNii Articles ID：120006888263, CiNii Books ID：AN00061013
■ Affiliated academic society
  • The London Mathematical Society
  • The Mathematical Society of Japan
■ Research projects
  • 基底状態の諸相に対する多角的探究の試み　　　　　　　　　　　　　　　
    01 Apr. 2022 - 31 Mar. 2027
    Grant amount(Total)：38740000, Direct funding：29800000, Indirect funding：8940000
    Grant number：22H00098
  • Investigating the stability of the inverse Brascamp-Lieb inequality　　　　　　　　　　　　　　　
    JSPS, Grant-in-Aid for Scientific Research (B), Apr. 2023 - Mar. 2027
    Neal Bez, Principal investigator
    Grant number：23K25777
  • Endpoint estimates for geometric maximal operators　　　　　　　　　　　　　　　
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for JSPS Fellows, Nov. 2023 - Mar. 2026
    Saitama University
    Grant amount(Total)：1600000, Direct funding：1600000
    Grant number：23KF0188
  • 古典場の理論における微分型相互作用の数学解析　　　　　　　　　　　　　　　
    01 Apr. 2019 - 31 Mar. 2024
    Grant amount(Total)：43680000, Direct funding：33600000, Indirect funding：10080000
    Grant number：19H00644
  • Research on Dispersive Equations and Harmonic Analysis　　　　　　　　　　　　　　　
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Fund for the Promotion of Joint International Research (Fostering Joint International Research (B)), 09 Oct. 2018 - 31 Mar. 2023
    Waseda University
    Grant amount(Total)：17810000, Direct funding：13700000, Indirect funding：4110000
    Grant number：18KK0073
  • New perspectives on space-time estimates for dispersive equations　　　　　　　　　　　　　　　
    JSPS, Grant-in-Aid for Scientific Research (B), Apr. 2019 - Mar. 2023
    Neal Bez, Principal investigator
    Grant number：19H01796
  • New developments on the restriction conjecture for the Fourier transform using multilinear analysis　　　　　　　　　　　　　　　
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for JSPS Fellows, 25 Apr. 2018 - 31 Mar. 2020
    Saitama University
    Grant amount(Total)：1500000, Direct funding：1500000
    Grant number：18F18020
  • Study on null forms in global space-time in the framework of equalities　　　　　　　　　　　　　　　
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Challenging Exploratory Research, 01 Apr. 2016 - 31 Mar. 2020
    Ozawa Tohru, Waseda University
    Grant amount(Total)：3640000, Direct funding：2800000, Indirect funding：840000
    Stability of trace theorems on the sphere is studied as the most fundamental subject in the research of null forms in global space-time. We have established the desired optimal inequalities for the stability theory and given its characterization from the viewpoint of duality. Regarding the Hardy and Rellich inequalities, we have formulated their equality framework with explicit remainder terms, therely we were able to recast the associated best constants and extremizers in a direct and explicit understanding. This provides a new method, independent of implicit arguments of contradiction and compactness.
    Grant number：16K13771
  • Conjectures associated with Brascamp-Lieb type inequalities　　　　　　　　　　　　　　　
    JSPS, Grant-in-Aid for Young Scientists (A), Apr. 2016 - Mar. 2019
    Neal Bez, Principal investigator
    Competitive research funding, Grant number：16H05995
  • New frontiers in kinetic equation theory　　　　　　　　　　　　　　　
    JSPS, Grant-in-Aid for Research Activity Start-up, Aug. 2014 - Mar. 2016
    Neal Bez, Principal investigator
    Competitive research funding, Grant number：26887008
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