Journal of the London Mathematical Society



HÖRMANDER'S $H^p$ MULTIPLIER THEOREM FOR THE HEISENBERG GROUP


CHIN-CHENG LIN a1
a1 Department of Mathematics, National Central University, Chung-Li, Taiwan 320 clin@math.ncu.edu.tw

Abstract

Let $\Bbb H^n$ denote the (2n+1)-dimensional Heisenberg group. Given an operator-valued function $M$, define the operator $T_{M}$ by $(T_{M}f)\hat{\vphantom{f}}=\skew4\hat{f} M$ with ‘$\hat{}$’ denoting the Fourier transform. Hörmander-type sufficient conditions are determined on $M$ for the $H^p$-boundedness, $p\le 1$, of the operator $T_{M}$ on $\Bbb H^n$.

(Received May 29 2001)
(Revised February 13 2002)

Maths Classification

42B15; 42B30 (primary); 43A17 (secondary).