Naoto Shida

activity

20192024

most citedOn the ranges of bilinear pseudo-differential operators of

S_{0, 0}

-type on

L^{2} \times L^{2}

1 citations · 1 across the 9 of their papers we have counts for

collaborators

9 papers

math.CA2024

On some bilinear Fourier multipliers with oscillating factors, II

Tomoya Kato, Akihiko Miyachi, Naoto Shida +1

For $s > 0$ , $s \neq = 1$ , bilinear Fourier multipliers of the form $e^{i (∣ ξ ∣^{s} + ∣ η ∣^{s} + ∣ ξ + η ∣^{s})} σ (ξ, η)$ are considered, where $σ (ξ, η)$ belongs to the Hörmander class $S^{m}_{1…

math.CA2024

On some bilinear Fourier multipliers with oscillating factors, I

Tomoya Kato, Akihiko Miyachi, Naoto Shida +1

Bilinear Fourier multipliers of the form $e^{i (∣ ξ ∣ + ∣ η ∣ + ∣ ξ + η ∣)} σ (ξ, η)$ are considered. It is proved that if $σ (ξ, η)$ is in the Hörmander class $S^{m}_{1,0} (\mathbb{R}^{2n})…

math.CA2024

Bilinear oscillatory Fourier multipliers

Tomoya Kato, Akihiko Miyachi, Naoto Shida +1

For bilinear Fourier multipliers that contain some oscillatory factors, boundedness of the operators between Lebesgue spaces is given including endpoint cases. Sharpness of the res…

math.CA2023

Boundedness of multilinear pseudo-differential operators with $S_{0, 0}$ class symbols on Besov spaces

Naoto Shida

We consider multilinear pseudo-differential operators with symbols in the multilinear Hörmander class $S_{0, 0}$ . The aim of this paper is to discuss the boundedness of these operat…

math.CA2023

Boundedness of bilinear pseudo-differential operators with $B S_{0, 0}^{m}$ symbols on Sobolev spaces

Naoto Shida

In the present paper, bilinear pseudo-differential operators with symbols in the bilinear Hörmander class $B S_{0, 0}^{m}$ are considered. In particular, the boundedness of these opera…

math.CA2021

A remark on the relationship $1/ p = 1/ p_{1} + 1/ p_{2}$ for boundedness of bilinear pseudo-differential operators with exotic symbols

Tomoya Kato, Naoto Shida

We consider the bilinear pseudo-differential operators with symbols in the bilinear Hörmander classes $B S_{ρ, ρ}^{m}$ , $0 < ρ < 1$ . In this paper, we show that the condition $1/p = 1/…

math.CA2020

Kato-Ponce type inequality for bilinear pseudo-differential operators of $S_{0, 0}$ -type in the scale of Besov spaces

Naoto Shida

We consider the Kato-Ponce type inequality for bilinear pseudo-differential operators with $S_{0, 0}$ -type symbols in the scale of Besov spaces. In particular, the borderline whethe…

math.CA2020★ 1 cited

On the ranges of bilinear pseudo-differential operators of $S_{0, 0}$ -type on $L^{2} \times L^{2}$

Naoki Hamada, Naoto Shida, Naohito Tomita

In this paper, the ranges of bilinear pseudo-differential operators of $S_{0, 0}$ -type on $L^{2} \times L^{2}$ are determined in the framework of Besov spaces. Our result improves the $…

math.CA2019

Limited smoothness conditions with mixed norms for bilinear Fourier multipliers

Akihiko Miyachi, Naoto Shida, Naohito Tomita

In this paper, the $L^{2} \times L^{\infty} \to L^{2}$ and $L^{2} \times L^{2} \to L^{1}$ boundedness of bilinear Fourier multiplier operators is discussed under weak smoothness conditions o…

On some bilinear Fourier multipliers with oscillating factors, II

On some bilinear Fourier multipliers with oscillating factors, I

Bilinear oscillatory Fourier multipliers

Boundedness of multilinear pseudo-differential operators with S0,0​ class symbols on Besov spaces

Boundedness of bilinear pseudo-differential operators with BS0,0m​ symbols on Sobolev spaces

A remark on the relationship 1/p=1/p1​+1/p2​ for boundedness of bilinear pseudo-differential operators with exotic symbols

Kato-Ponce type inequality for bilinear pseudo-differential operators of S0,0​-type in the scale of Besov spaces

On the ranges of bilinear pseudo-differential operators of S0,0​-type on L2×L2

Limited smoothness conditions with mixed norms for bilinear Fourier multipliers

Boundedness of multilinear pseudo-differential operators with $S_{0, 0}$ class symbols on Besov spaces

Boundedness of bilinear pseudo-differential operators with $B S_{0, 0}^{m}$ symbols on Sobolev spaces

A remark on the relationship $1/ p = 1/ p_{1} + 1/ p_{2}$ for boundedness of bilinear pseudo-differential operators with exotic symbols

Kato-Ponce type inequality for bilinear pseudo-differential operators of $S_{0, 0}$ -type in the scale of Besov spaces

On the ranges of bilinear pseudo-differential operators of $S_{0, 0}$ -type on $L^{2} \times L^{2}$