Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T16:05:33.559Z Has data issue: false hasContentIssue false
  • English
  • Français

HILBERT TRANSFORMS ALONG CURVES IN THE HEISENBERG GROUP

Published online by Cambridge University Press:  20 August 2001

JOONIL KIM
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)