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HILBERT TRANSFORMS ALONG CURVES IN THE HEISENBERG GROUP

  • JOONIL KIM

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.

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HILBERT TRANSFORMS ALONG CURVES IN THE HEISENBERG GROUP

  • JOONIL KIM

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