Boundedness criterion for bilinear Fourier multiplier operators

Abstract

Bilinear Fourier multiplier operators corresponding to multipliers that are singular at the origin are considered. New criterions on such multipliers to assure the boundedness of the corresponding operators from $L^p \times L^q$ to $L^r$, $1/p+1/q=1/r$, are given in the range $1<p,q \le \infty$, $2/3<r<\infty$.