Journal of the
Korean Mathematical Society JKMS

Demeter \cite{d} and Kuk and Lee \cite{kl} proved the unboundedness of the trilinear Hilbert transforms $H_{a,b,c}$ under the critical index $1/2$ for some parameters $a,b$ and $c$. We show the unboundedness of $H_{a,b,c}$ for any parameters.

Keywords: Bilinear Hilbert transform, trilinear Hilbert transform, trilinear fractional integral operator

MSC numbers: Primary 42B20