Spectral multipliers for sub-Laplacians: recent developments and open problems

Abstract: I will present some old and new results about the $L^p$ functional calculus for sub-Laplacians $L$. It has been known for a long time that, under quite general assumptions on the sub-Laplacian and the underlying sub-Riemannian structure, an operator of the form $F(L)$ is bounded on $L^p$, $1< p<\infty$, whenever the multiplier $F$ satisfies a scale-invariant smoothness condition of sufficiently larger order. The problem of determining the minimal smoothness assumptions, however, remains widely open and will be the focus of our discussion.

classical analysis and ODEsfunctional analysisrepresentation theoryspectral theory

Audience: researchers in the topic

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