$L^p$ bounds for spectral multipliers on rank one NA-groups with roots not all positive
Volume 101 / 2004
Colloquium Mathematicum 101 (2004), 51-74
MSC: Primary 22E30; Secondary 22E25, 43A15, 43A80, 47A60, 47D05.
DOI: 10.4064/cm101-1-4
Abstract
We consider a family of non-unimodular rank one $NA$-groups with roots not all positive, and we show that on these groups there exists a distinguished left invariant sub-Laplacian which admits a differentiable $L^p$ functional calculus for every $p\ge 1$.
