Unboundedness of the trilinear Hilbert transform under the critical index
J. Korean Math. Soc. 2021 Vol. 58, No. 5, 1299-1309
Published online May 14, 2021
Printed September 1, 2021
Yasuo Komori-Furuya
Tokai University
Abstract : 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
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