On the 𝐿²→𝐿^{∞} norms of spectral multipliers of “quasi-homogeneous” operators on homogeneous groups

Sikora, Adam

doi:10.1090/S0002-9947-99-02501-5

On the $L^2\rightarrow L^\infty$ norms of spectral multipliers of “quasi-homogeneous” operators on homogeneous groups
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Trans. Amer. Math. Soc. 351 (1999), 3743-3755 Request permission

Abstract:

We study the $L^2 \to L^{\infty }$ norms of spectral projectors and spectral multipliers of left-invariant elliptic and subelliptic second-order differential operators on homogeneous Lie groups. We obtain a precise description of the $L^2 \to L^{\infty }$ norms of spectral multipliers for some class of operators which we call quasi-homogeneous. As an application we prove a stronger version of Alexopoulos’ spectral multiplier theorem for this class of operators.

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