Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth
Volume 111 / 1994
Studia Mathematica 111 (1994), 103-121 DOI: 10.4064/sm-111-2-103-121
We prove that on Iwasawa AN groups coming from arbitrary semisimple Lie groups there is a Laplacian with a nonholomorphic functional calculus, not only for $L^1(AN),$ but also for $L^p(AN)$, where 1 < p < ∞. This yields a spectral multiplier theorem analogous to the ones known for sublaplacians on stratified groups.