双线性Fourier乘子在模空间中的正交性

Orthogonality of the bilinear Fourier multiplier in the modulation spaces

本文证明了,如果一列在模空间一致有界的双线性Fourier乘子具有一定的正交性,则这列双线性算子的和仍然在模空间中有界.同时,本文给出了双线性Fourier乘子在模空间上有界的等价刻画.

In this paper, we consider the boundedness of the bilinear Fourier multipliers on modulation spaces.We prove that if a family of bilinear Fourier multipliers is bounded and has some orthogonality, the sum of these bilinear Fourier multipliers is also bounded on modulation spaces. As a corollary, we give the necessary and sufficient conditions for the boundedness of bilinear Fourier multipliers.