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Journal of Lie Theory 17 (2007), No. 1, 163--189
Copyright Heldermann Verlag 2007

Spectral Multipliers on Damek-Ricci Spaces

Maria Vallarino
Dip. di Matematica e Applicazioni, UniversitÓ di Milano Bicocca, Via R. Cozzi 53, 20125 Milano, Italy


Let $S$ be a Damek--Ricci space, and $\Delta$ be a distinguished Laplacean on $S$ which is left invariant and selfadjoint in $L^2(\rho)$. We prove that $S$ is a Calder\'on-Zygmund space with respect to the right Haar measure $\rho$ and the left invariant distance. We give sufficient conditions of H\"ormander type on a multiplier $m$ so that the operator $m(\Delta)$ is bounded on $L^p(\rho)$ when $1
Keywords: Multipliers, singular integrals, Calderon-Zygmund decomposition, Damek-Ricci spaces.

MSC: 22E30, 42B15, 42B20, 43A80

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