Research

・Interests

Harmonic analysis, PDE, geometric analysis

・Publications

arXiv

A note on ubiquity of geometric Brascamp-Lieb data
with A. Gauvan, H. Tsuji, Bulletin of the London Mathematical Society, to appear

Orthonormal Strichartz estimates for the wave equation and related geometric inequalities
with S. Lee, S. Nakamura, ICIAM Proceedings, to appear

Boundary Strichartz estimates and pointwise convergence for orthonormal systems
with S. Kinoshita, S. Shiraki, Transactions of the London Mathematical Society, to appear

A note on Strichartz estimates for the wave equation with orthonormal initial data
with S. Kinoshita, S. Shiraki, RIMS Kokyuroku Bessatsu, to appear

Regularized Brascamp-Lieb inequalities
with S. Nakamura, Analysis & PDE, to appear

Stability of hypercontractivity, the logarithmic Sobolev inequality, and Talagrand's cost inequality
with S. Nakamura, H. Tsuji, Journal of Functional Analysis, 285 (2023), 110121, 66 pp

Revisiting the Rellich inequality
with S. Machihara, T. Ozawa, Mathematische Zeitschrift, 303 (2023), Article 49

Fourier制限予想と掛谷予想ー最近の発展ー
数学, 74 (2022), 337-355

Higher order transversality in harmonic analysis
with J. Bennett, RIMS Kokyuroku Bessatsu, B88 (2021), 75-103

Strichartz estimates for orthonormal families of initial data and weighted oscillatory integral estimates
with S. Lee, S. Nakamura, Forum of Mathematics, Sigma, 9 (2021), e1

On the nonlinear Brascamp-Lieb inequality
with J. Bennett, S. Buschenhenke, M. Cowling, T. Flock, Duke Mathematical Journal, 169 (2020), 3291-3338

The nonlinear Brascamp-Lieb inequality for simple data
with J. Bennett, S. Buschenhenke, T. Flock, not intended for publication (subsumed by above)

Maximal estimates for the Schrodinger equation with orthonormal initial data
with S. Lee, S. Nakamura, Selecta Mathematica, 26 (2020), Article 52

A supersolutions perspective on hypercontractivity
with Y. Aoki, J. Bennett, S. Machihara, K. Matsuura, S. Shiraki, Annali di Matematica Pura ed Applicata, 199 (2020), 2105-2116

Inhomogeneous Strichartz estimates in some critical cases
with J. Cunanan, S. Lee, Proceedings of the American Mathematical Society, 148 (2020), 639-652

Hardy type inequalities with spherical derivatives
with S. Machihara, T. Ozawa, SN Partial Differential Equations and Applications, 1 (2020), Article 5

On the Strichartz estimates for orthonormal systems of initial data with regularity
with Y. Hong, S. Lee, S. Nakamura, Y. Sawano, Advances in Mathematics, 354 (2019), 106736, 37 pp

Smoothing estimates for velocity averages with radial data
with J. Cunanan, RIMS Kokyuroku Bessatsu, B74 (2019), 33-46

Generating monotone quantities for the heat equation
with J. Bennett, Journal fur die Reine und Angewandte Mathematik, 756 (2019), 37-63

Remarks on the Mizohata-Takeuchi conjecture and related problems
with M. Sugimoto, Asympototic Analysis for Nonlinear Dispersive and Wave Equations, Advanced Studies in Pure Mathematics, 81 (2019), 1-12

Smoothing estimates for the kinetic transport equation at the critical regularity
with J. Cunanan, S. Lee, SIAM Journal on Mathematical Analysis, 50 (2018), 2280 -2294

A sharp k-plane Strichartz inequality for the Schrodinger equation
with J. Bennett, T. Flock, S. Gutierrez, M. Iliopoulou, Transactions of the American Mathematical Society, 370 (2018), 5617-5633

Stability of trace theorems on the sphere
with C. Jeavons, T. Ozawa, M. Sugimoto, Journal of Geometric Analysis, 28 (2018), 1456-1476

Estimates for the kinetic transport equation in hyperbolic Sobolev spaces
with J. Bennett, S. Gutierrez, S. Lee, Journal de Mathematiques Pures et Appliquees, 114 (2018), 1-28.

Stability of the Brascamp-Lieb constant and applications
with J. Bennett, T. Flock, S. Lee, American Journal of Mathematics, 140 (2018), 543-569

Behaviour of the Brascamp-Lieb constant
with J. Bennett, M. Cowling, T. Flock, Bulletin of the London Mathematical Society, 49 (2017), 512-518

Sharpness of the Brascamp-Lieb inequality in Lorentz spaces
with S. Lee, S. Nakamura, Y. Sawano, Electronic Research Announcements in Mathematical Sciences, 24 (2017), 53-63

A conjecture regarding optimal Strichartz estimates for the wave equation
with C. Jeavons, T. Ozawa, H. Saito, New Trends in Analysis and Interdisciplinary Applications, Trends in Mathematics, Springer (2017), 293-300

On sharp bilinear Strichartz estimates of Ozawa-Tsutsumi type
with J. Bennett, C. Jeavons, N. Pattakos, Journal of the Mathematical Society of Japan, 69 (2017), 459-476

Optimal constants and extremisers for some smoothing estimates
with M. Sugimoto, Journal d'Analyse Mathematique, 131 (2017), 159-187

Some sharp bilinear space-time estimates for the wave equation
with C. Jeavons, T. Ozawa, Mathematika, 62 (2016), 719-737

A survey on optimal smoothing estimates and trace theorems
with M. Sugimoto, Advances in Mathematics (China), 45 (2016), 801-816

Extremisers for trace estimates on the sphere
with S. Machihara, M. Sugimoto, Mathematical Research Letters, 23 (2016), 633-647

Flow monotonicity and Strichartz inequalities
with J. Bennett, M. Iliopoulou, International Mathematics Research Notices, 19 (2015), 9415-9437

Some recent progress on sharp Kato-type smoothing estimates
with M. Sugimoto, Israel Mathematical Conference Proceedings, Complex Analysis and Dynamical Systems VI: Part 1: PDE, Differential Geometry, Radon Transform, Contemporary Mathematics, 653 (2015), 41-50

Applications of the Funk-Hecke theorem to smoothing and trace estimates
with H. Saito, M. Sugimoto, Advances in Mathematics, 285 (2015), 1767-1795

Optimal forward and reverse estimates of Morawetz and Kato-Yajima type with angular smoothing index
with M. Sugimoto, Journal of Fourier Analysis and Applications, 21 (2015), 318-341

A sharp Sobolev-Strichartz estimate for the wave equation
with C. Jeavons, Electronic Research Announcements in Mathematical Sciences, 22 (2015), 46-54

Sharp Sobolev-Strichartz estimates for the free Schrodinger propagator
with C. Jeavons, N. Pattakos, Current Trends in Analysis and its Applications, Birkhauser, 2015, 281-288

A note on magnitude bounds for the mask coefficients of the interpolatory Dubuc-Deslauriers subdivision scheme
with H. E. Bez, LMS Journal of Computation and Mathematics, 17 (2014), 226-232

On the Strichartz estimates for the kinetic transport equation
with J. Bennett, S. Gutierrez, S. Lee, Communications in Partial Differential Equations, 39 (2014), 1821-1826

Optimal constant for a smoothing estimate of critical index
with M. Sugimoto, Fourier Analysis, Trends in Mathematics, Birkhauser/Springer, 2014, 1-7

A sharp Strichartz estimate for the wave equation with data in the energy space
with K. Rogers, Journal of the European Mathematical Society, 15 (2013), 805-823

On derivative bounds for the rational quadratic Bezier paths
with H. E. Bez, Computer Aided Geometric Design, 30 (2013), 254-261

New minimal bounds for the derivatives of rational Bezier paths and rational rectangular Bezier surfaces
with H. E. Bez, Applied Mathematics and Computation, 225 (2013), 475-479

Transversal multilinear Radon-like transforms: local and global estimates
with J. Bennett, S. Gutierrez, Revista Matematica Iberoamericana, 29 (2013), 756-788

Global nonlinear Brascamp-Lieb inequalities
with J. Bennett, S. Gutierrez, Journal of Geometric Analysis, 23 (2013), 1806-1817

A majorant problem for the periodic Schrodinger group
with J. Bennett, Harmonic Analysis and Nonlinear Partial Differential Equations, RIMS Kokyuroku Bessatsu B33 (2012), 1-10

Some nonlinear Brascamp-Lieb inequalities and applications to harmonic analysis
with J. Bennett, Journal of Functional Analysis, 259 (2010), 2520-2556

Maximal operators and Hilbert transforms along flat curves near L^1
Journal of the Australian Mathematical Society, 87 (2009), 311-323

Maximal operators along piecewise linear curves near L^1
Indiana University Mathematics Journal, 58 (2009), 1639-1658

Heat-flow monotonicity of Strichartz norms
with J. Bennett, A. Carbery, D. Hundertmark, Analysis & PDE 2 (2009), 147-158

Heat-flow monotonicity underlying some sharp inequalities in geometric and harmonic analysis
Harmonic Analysis and Nonlinear Partial Differential Equations, RIMS Kokyuroku Bessatsu B14 (2009), 1-15

Heat-flow monotonicity related to the Hausdorff-Young inequality
with J. Bennett, A. Carbery, Bulletin of the London Mathematical Society 41 (2009), 971-979

Closure properties of solutions to heat inequalities
with J. Bennett, Journal of Geometric Analysis, 19 (2009), 584-600

Mixed-norm estimates for a class of nonisotropic directional maximal operators and Hilbert transforms
Journal of Functional Analysis, 255 (2008), 3281-3302

L^p-boundedness for the Hilbert transform and maximal operator along a class of nonconvex curves
Proceedings of the American Mathematical Society, 135 (2007), 151-161