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42b30 (primary)

Journal of the London Mathematical Society (1)

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HÖRMANDER'S $H^p$ MULTIPLIER THEOREM FOR THE HEISENBERG GROUP
CHIN-CHENG LIN
Journal:

Journal of the London Mathematical Society / Volume 67 / Issue 3 / June 2003

Published online by Cambridge University Press:

20 May 2003, pp. 686-700

Print publication:

June 2003
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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 $\Bbb H^n$.