Tomoya Kato

activity

20172024

most citedBoundedness of multilinear pseudo-differential operators of

S_{0, 0}

-type in

L^{2}

-based amalgam spaces

5 citations · 11 across the 17 of their papers we have counts for

collaborators

18 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

Estimates for a certain bilinear Fourier integral operator

Tomoya Kato, Akihiko Miyachi, Naohito Tomita

In this paper, we consider the boundedness from $H^{1} \times L^{\infty}$ to $L^{1}$ of bilinear Fourier integral operators with non-degenerate phase functions and amplitudes in $B…

math.CA2023

Estimates for some bilinear wave operators

Tomoya Kato, Akihiko Miyachi, Naohito Tomita

We consider some bilinear Fourier multiplier operators and give a bilinear version of Seeger, Sogge, and Stein's result for Fourier integral operators. Our results improve, for the…

math.CA2022

Multilinear pseudo-differential operators with $S_{0, 0}$ class symbols of limited smoothness

Tomoya Kato

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

math.CA2021

Notes on bilinear lattice bump Fourier multipliers

Tomoya Kato, Akihiko Miyachi, Naohito Tomita

We consider the bilinear Fourier multiplier operator with the multiplier written as a linear combination of a fixed bump function. For those operators we prove two transference the…

math.CA2021

Boundedness of multilinear pseudo-differential operators with symbols in the Hörmander class $S_{0, 0}$

Tomoya Kato, Akihiko Miyachi, Naohito Tomita

The multilinear pseudo-differential operators with symbols in the multilinear Hörmander class $S_{0, 0}$ are considered. A complete identification of the cases where those operators…

math.CA2021

Boundedness of bilinear pseudo-differential operators of $S_{0, 0}$ -type in Wiener amalgam spaces and in Lebesgue spaces

Tomoya Kato, Akihiko Miyachi, Naohito Tomita

We extend and improve the known results about the boundedness of the bilinear pseudo-differential operators with symbols in the bilinear Hörmander class $BS^{m}_{0,0}(\mathbb{R}^n)…

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

Notes on lattice bump Fourier multiplier operators on $L^{2} \times L^{2}$

Tomoya Kato, Akihiko Miyachi, Naohito Tomita

Given a smooth bump function, we consider the multiplier formed by taking the linear combination of the translations of the bump function and the corresponding bilinear Fourier mul…

math.CA2020

A remark on bilinear pseudo-differential operators with symbols in the Sjöstrand class

Tomoya Kato

In this short note, we consider bilinear pseudo-differential operators with symbols belonging to the Sjöstrand class. We show that those operators are bounded from the product of t…

math.CA2020★ 3 cited

Bilinear pseudo-differential operators with exotic class symbols of limited smoothness

Tomoya Kato

We consider bilinear pseudo-differential operators with symbols in the bilinear Hörmander class, $B S_{ρ, ρ}^{m}$ , $m \in R$ , $0 \leq ρ < 1$ . The aim of this paper is to discu…

math.CA2019★ 5 cited

Boundedness of multilinear pseudo-differential operators of $S_{0, 0}$ -type in $L^{2}$ -based amalgam spaces

Tomoya Kato, Akihiko Miyachi, Naohito Tomita

We consider the multilinear pseudo-differential operators with symbols in a generalized $S_{0, 0}$ -type class and prove the boundedness of the operators from $(L^2,\ell^{q_1}) \time…

math.CA2019

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

Tomoya Kato, Akihiko Miyachi, Naohito Tomita

We extend the known result that the bilinear pseudo-differential operators with symbols in the bilinear Hörmander class $B S_{0, 0}^{- n /2} (R^{n})$ are bounded from $L^2 \times…

math.FA2018★ 1 cited

Nonlinear operations on a class of modulation spaces

Tomoya Kato, Mitsuru Sugimoto, Naohito Tomita

We discuss when the nonlinear operation $f \mapsto F (f)$ maps the modulation space $M_{s}^{p, q} (R^{n})$ ( $1 \leq p, q \leq \infty$ ) to the same space again. It is known that $M^…

math.FA2017★ 2 cited

A remark on the Schrödinger operator on Wiener amalgam spaces

Tomoya Kato, Naohito Tomita

In this paper, we study the boundedness of the Schrödinger operator $e^{i Δ}$ on Wiener amalgam spaces and determine its optimal condition.

math.FA2017

Pseudodifferential operators with symbols in the Hörmander class $S_{α, α}^{0}$ on $α$ -modulation spaces

Tomoya Kato, Naohito Tomita

In this paper, we study the boundedness of pseudodifferential operators with symbols in the Hörmander class $S_{ρ, ρ}^{0}$ on $α$ -modulation spaces $M_{p, q}^{s, α}$ , and consider the r…

On some bilinear Fourier multipliers with oscillating factors, II

On some bilinear Fourier multipliers with oscillating factors, I

Bilinear oscillatory Fourier multipliers

Estimates for a certain bilinear Fourier integral operator

Estimates for some bilinear wave operators

Multilinear pseudo-differential operators with S0,0​ class symbols of limited smoothness

Notes on bilinear lattice bump Fourier multipliers

Boundedness of multilinear pseudo-differential operators with symbols in the Hörmander class S0,0​

Boundedness of bilinear pseudo-differential operators of S0,0​-type in Wiener amalgam spaces and in Lebesgue spaces

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

Notes on lattice bump Fourier multiplier operators on L2×L2

A remark on bilinear pseudo-differential operators with symbols in the Sjöstrand class

Bilinear pseudo-differential operators with exotic class symbols of limited smoothness

Boundedness of multilinear pseudo-differential operators of S0,0​-type in L2-based amalgam spaces

Boundedness of bilinear pseudo-differential operators of S0,0​-type on L2×L2

Nonlinear operations on a class of modulation spaces

A remark on the Schrödinger operator on Wiener amalgam spaces

Pseudodifferential operators with symbols in the Hörmander class Sα,α0​ on α-modulation spaces

Multilinear pseudo-differential operators with $S_{0, 0}$ class symbols of limited smoothness

Boundedness of multilinear pseudo-differential operators with symbols in the Hörmander class $S_{0, 0}$

Boundedness of bilinear pseudo-differential operators of $S_{0, 0}$ -type in Wiener amalgam spaces and in Lebesgue spaces

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

Notes on lattice bump Fourier multiplier operators on $L^{2} \times L^{2}$

Boundedness of multilinear pseudo-differential operators of $S_{0, 0}$ -type in $L^{2}$ -based amalgam spaces

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

Pseudodifferential operators with symbols in the Hörmander class $S_{α, α}^{0}$ on $α$ -modulation spaces