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arXiv · 1212.0775

Spectral multipliers on Heisenberg-Reiter and related groups

Alessio Martini
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Abstract

Let $L$ be a homogeneous sublaplacian on a 2-step stratified Lie group $G$ of topological dimension $d$ and homogeneous dimension $Q$. By a theorem due to Christ and to Mauceri and Meda, an operator of the form $F(L)$ is bounded on $L^p$ for $1 < p < \infty$ if $F$ satisfies a scale-invariant smoothness condition of order $s > Q/2$. Under suitable assumptions on $G$ and $L$, here we show that a smoothness condition of order $s > d/2$ is sufficient. This extends to a larger class of 2-step groups the results for the Heisenberg and related groups by Müller and Stein and by Hebisch, and for the free group $N_{3,2}$ by Müller and the author.

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Alessio Martini. 2012-12-04. Spectral multipliers on Heisenberg-Reiter and related groups. https://doi.org/10.1007/s10231-014-0414-6

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