Riesz transforms and Lie groups of polynomial growth
A. F. M. ter Elst, Derek W. Robinson, Adam Sikora · 1998
Let G be a Lie group of polynomial growth. We prove that the second-order Riesz transforms onL2(G; dg) are bounded if, and only if, the group is a direct product of a compact group and a nilpotent group, in which case the transforms of all orders are bounded.