Akihiko Miyachi

activity

20182024

most citedBoundedness of multilinear pseudo-differential operators of

S_{0, 0}

-type in

L^{2}

-based amalgam spaces

5 citations · 9 across the 14 of their papers we have counts for

collaborators

14 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.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.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.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…

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.CA2018

Bilinear pseudo-differential operators with exotic symbols, II

Akihiko Miyachi, Naohito Tomita

The boundedness from $H^{p} \times L^{2}$ to $L^{r}$ , $1/ p + 1/2 = 1/ r$ , and from $H^{p} \times L^{\infty}$ to $L^{p}$ of bilinear pseudo-differential operators is proved under the assumption th…

math.CA2018★ 4 cited

Bilinear pseudo-differential operators with exotic symbols

Akihiko Miyachi, Naohito Tomita

The boundedness from $L^{p} \times L^{q}$ to $L^{r}$ , $1 < p, q \leq \infty$ , $0 < 1/ p + 1/ q = 1/ r \leq 1$ , of bilinear pseudo-differential operators with symbols in the bilinear Hörmander class $B…

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

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

Notes on lattice bump Fourier multiplier operators on L2×L2

Limited smoothness conditions with mixed norms for bilinear Fourier multipliers

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

Bilinear pseudo-differential operators with exotic symbols, II

Bilinear pseudo-differential operators with exotic symbols

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

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