Riesz transforms on generalized Heisenberg groups and Riesz transforms associated to the CCR heat flow (Q1768138)

Inspired by a method of \textit{G. Pisier} [Riesz transforms: A simpler analytic proof of P. A. Meyer's inequality. Séminaire de probabilités XXII, Strasbourg/France, Lect. Notes Math. 1321, 485--501 (1988; Zbl 0645.60061)], the author obtains here estimates for the norm of the Riesz transforms \(R_k\) in two different settings: in the first case the Riesz transforms act on \(L^q(G)\), \(1< q<\infty\), where \(G\) is a generalized Heisenberg group. In the second case the Riesz transforms act on the Schatten space \(S_q(H)\), defined by commuting inner *-derivations on the \(C^*\)-algebra \(K(H)\) of compact operators on a Hilbert space \(H\).