Journal of Lie Theory

no. 1
Spectral Multipliers on Damek-Ricci Spaces
Journal of Lie Theory, Volume 17 (2007) no. 1, pp. 163-189
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 $1$, and of weak type $(1,1)$.
DOI: 10.5802/jolt.442
Classification: 22E30, 42B15, 42B20, 43A80
Keywords: Multipliers, singular integrals, Calderon-Zygmund decomposition, Damek-Ricci spaces 
@article{JOLT_2007_17_1_a9,
     author = {M. Vallarino},
     title = {Spectral {Multipliers} on {Damek-Ricci} {Spaces}},
     journal = {Journal of Lie Theory},
     pages = {163--189},
     year = {2007},
     volume = {17},
     number = {1},
     doi = {10.5802/jolt.442},
     zbl = {1124.22002},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.442/}
}
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M. Vallarino. Spectral Multipliers on Damek-Ricci Spaces. Journal of Lie Theory, Volume 17 (2007) no. 1, pp. 163-189. doi: 10.5802/jolt.442

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