On the L~2 -> L~infinity norms of spectral multipliers of 'Quasi-Homogeneous' operators on homogeneous groups

摘要

We study the L~2 -> L~infinity 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 -> L~infinity 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.