Naohito Tomita

Minimal smoothness conditions for bilinear Fourier multipliers.

The problem of finding the differentiability conditions for bilinear Fourier multipliers that are as small as possible to ensure the boundedness of the corresponding operators from products of Hardy spaces H1 ×Hp2 to L, 1/p1 + 1/p2 = 1/p, is considered. The minimal conditions in terms of the product type Sobolev norms are given for the whole range 0 < p1, p2 ≤ ∞.

Weighted norm inequalities for multilinear Fourier multipliers

In this paper, we consider weighted norm inequalities for multilinear Fourier multipliers. Our result can be understood as a multilinear version of the result by Kurtz and Wheeden.

On Multilinear Fourier Multipliers of Limited Smoothness

In this paper, we prove the L2-boundedness of multilinear Fourier multiplier operators with multipliers of limited smoothness. As a result, we can extend Calderón and Torchinsky’s result in the linear theory to the multilinear case. The sharpness of our results is also discussed.

A counterexample for boundedness of pseudo-differential operators on modulation spaces

We prove that pseudo-differential operators with symbols in the class S 0 1,δ (0 < δ < 1) are not always bounded on the modulation space M p,q (q ≠2) .

Bilinear pseudo-differential operators with exotic symbols, II

The boundedness from

Boundedness Properties of Pseudo-Differential and Calderón-Zygmund Operators on Modulation Spaces

H^p \times L^2

Boundedness criterion for bilinear Fourier multiplier operators

Hp×L2 to