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HILBERT TRANSFORMS ALONG CURVES IN THE HEISENBERG GROUP

Published online by Cambridge University Press:  20 August 2001

JOONIL KIM
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Abstract

We consider Hilbert transforms along curves $\Gamma$ on the Heisenberg group. In particular, necessary and sufficient conditions for the $L^2$-boundedness are given for $\Gamma(t)=(t,\gamma(t),0)$ when $\gamma$ is even or odd and convex on ${\Bbb R}^{+}$. 1991 Mathematics Subject Classification: 42B20,42B25.

Keywords

Hilbert transformHeisenberg groupgroup Fourier transformdoubling propertyalmost orthogonality
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 80 , Issue 3 , May 2000 , pp. 611 - 642
Copyright
1999 London Mathematical Society

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