Unboundedness of the trilinear Hilbert transform under the critical index
J. Korean Math. Soc.
Published online May 14, 2021
Yasuo Komori-Furuya
Tokai University
Abstract : Demeter (2008) and Kuk and Lee (2012) 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 : 42B20
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