57 citations · 74 across the 15 of their papers we have counts for
15 papers
Hypercontractivity beyond Nelson's time and its applications to Blaschke--Santaló inequality and inverse Santaló inequality
Shohei Nakamura, Hiroshi Tsuji
We explore an interplay between an analysis of diffusion flows such as Ornstein--Uhlenbeck flow and Fokker--Planck flow and inequalities from convex geometry regarding the volume p…
Decoupling inequality for paraboloid under shell type restriction and its application to the periodic Zakharov system
Shinya Kinoshita, Shohei Nakamura, Akansha Sanwal
In this paper, we establish local well-posedness for the Zakharov system on , in a low regularity setting. Our result improves the work of Kishimoto. Moreover…
Stability of hypercontractivity, the logarithmic Sobolev inequality, and Talagrand's cost inequality
Neal Bez, Shohei Nakamura, Hiroshi Tsuji
We provide deficit estimates for Nelson's hypercontractivity inequality, the logarithmic Sobolev inequality, and Talagrand's transportation cost inequality under the restriction th…
Regularized Brascamp--Lieb inequalities
Neal Bez, Shohei Nakamura
Given any (forward) Brascamp--Lieb inequality on euclidean space, a famous theorem of Lieb guarantees that gaussian near-maximizers always exist. Recently, Barthe and Wolff used ma…
Tomography bounds for the Fourier extension operator and applications
Jonathan Bennett, Shohei Nakamura
We explore the extent to which the Fourier transform of an density supported on the sphere in can have large mass on affine subspaces, placing particular empha…
Strichartz estimates for orthonormal families of initial data and weighted oscillatory integral estimates
Neal Bez, Sanghyuk Lee, Shohei Nakamura
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 thos…
Maximal estimates for the Schrödinger equation with orthonormal initial data
Neal Bez, Sanghyuk Lee, Shohei Nakamura
For the one-dimensional Schrödinger equation, we obtain sharp maximal-in-time and maximal-in-space estimates for systems of orthonormal initial data. The maximal-in-time estimates…
Finite difference scheme for two-dimensional periodic nonlinear Schrödinger equations
Younghun Hong, Chulkwang Kwak, Shohei Nakamura +1
A nonlinear Schrödinger equation (NLS) on a periodic box can be discretized as a discrete nonlinear Schrödinger equation (DNLS) on a periodic cubic lattice, which is a system of fi…
The orthonormal Strichartz inequality on torus
Shohei Nakamura
In this paper, motivated by recent important works due to Frank-Lewin-Lieb-Seiringer \cite{FLLS} and Frank-Sabin \cite{frank-sabin-1}, we study the Strichartz inequality on torus w…
On the Strichartz estimates for orthonormal systems of initial data with regularity
Neal Bez, Younghun Hong, Sanghyuk Lee +2
The classical Strichartz estimates for the free Schrödinger propagator have recently been substantially generalised to estimates of the form \[ \bigg\|\sum_jλ_j|e^{itΔ}f_j|^2\bigg\…
Multiplier conditions for Boundedness into Hardy spaces
Loukas Grafakos, Shohei Nakamura, Hanh Van Nguyen +1
In the present work, we find useful and explicit necessary and sufficient conditions for linear and multilinear multiplier operators of Coifman-Meyer type, finite sum of products o…
Conditions for Boundedness into Hardy spaces
Loukas Grafakos, Shohei Nakamura, Hanh Van Nguyen +1
We obtain boundedness from a product of Lebesgue or Hardy spaces into Hardy spaces under suitable cancellation conditions for a large class of multilinear operators that includes t…
Fractional operators on weighted Morrey spaces
Shohei Nakamura, Yoshihiro Sawano, Hitoshi Tanaka
A necessary condition and a sufficient condition for one weight norm inequalities on Morrey spaces to hold are given for the fractional maximal operator and the fractional integral…
The singular integral operator and its commutator on weighted Morrey spaces
Shohei Nakamura, Yoshihiro Sawano
In this paper, we give necessary conditions and sufficient conditions respectively for the boundedness of the singular integral operator on the weighted Morrey spaces. We observe t…
Generalized Morrey spaces and trace operator
Shohei Nakamura, Takahiro Noi, Yoshihiro Sawano
The theory of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces is developed. Generalized Morrey spaces, which T. Mizuhara and E. Nakai proposed, are e…