Riesz transforms for the distinguished Laplacian on Damek-Ricci spaces and operator-valued multivariate spectral multipliers

Jie Liu, Alessio Martini

Let $\Delta ={\nabla }^{\ast }\nabla$ be the distinguished Laplacian on a Damek-Ricci space. We prove the $L^p$-boundedness of the vector of first-order Riesz transforms $\nabla {\Delta }^{-1/2}$ in…