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

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 $\Bbb H^n$.