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Hilbert Transforms Along Curves in the Heisenberg Group

Authors:	Kim Joonil

Institution:	G-2 Kwangmyeng Villa 129 Dongsoongdong Chongrogu Seoul Korea 110-510 jikim7030{at}hanmail.net

Abstract:	We consider Hilbert transforms along curves ${Gamma}$ on the Heisenberggroup. In particular, necessary and sufficient conditions forthe L²-boundedness are given for ${Gamma}$ (t)=(t, ${gamma}$ (t),0) when ${gamma}$ is evenor odd and convex on R⁺. 1991 Mathematics Subject Classification:42B20, 42B25.

Keywords:	Hilbert transform Heisenberg group group Fourier transform doubling property almost orthogonality
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