논문KCI 등재
Unboundedness of the trilinear Hilbert transform under the critical index
대한수학회 (The Korean Mathematical Society)|2021.09|대한수학회지 (Journal of the KMS)|제58권 제5호|pp. 1299-1309|DOI 10.4134/JKMS.j200656
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초록
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.
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.
참고문헌 (7)
- CIPRIAN DEMETER, "Divergence of combinatorial averages and the unboundedness of the trilinear Hilbert transform", Ergodic Theory and Dynamical Systems, 28(5), pp.1453~1464 (2008), Cambridge University Press (CUP)[DOI]
- Loukas Grafakos, "On multilinear fractional integrals", Studia Mathematica, 102(1), pp.49~56 (1992), Institute of Mathematics, Polish Academy of Sciences[DOI]
- Loukas Grafakos, "Some remarks on multilinear maps and interpolation", Mathematische Annalen, 319(1), pp.151~180 (2001), Springer Science and Business Media LLC[DOI]
- Carlos E. Kenig, "Multilinear estimates and fractional integration", Mathematical Research Letters, 6(1), pp.1~15 (1999), International Press of Boston[DOI]
- Seungwoo Kuk, "Endpoint bounds for multilinear fractional integrals", Mathematical Research Letters, 19(5), pp.1145~1154 (2012), International Press of Boston[DOI]
- M. Lacey, "Lp estimates on the bilinear Hilbert transform for 2 < p < 1", Ann. of Math, 146, pp.693~724 (1997)
- Michael Lacey, "On Calderon's Conjecture", The Annals of Mathematics, 149(2), pp.475~ (1999), JSTOR[DOI]
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