$L^p$-boundedness of Riesz transforms on solvable extensions of Carnot
groups
$L^p$-boundedness of Riesz transforms on solvable extensions of Carnot
groups
Let $G=N\rtimes \mathbb{R}$, where $N$ is a Carnot group and $\mathbb{R}$ acts on $N$ via automorphic dilations. Homogeneous left-invariant sub-Laplacians on $N$ and $\mathbb{R}$ can be lifted to $G$, and their sum is a left-invariant sub-Laplacian $\Delta$ on $G$. We prove that the first-order Riesz transforms $X \Delta^{-1/2}$ are bounded …