Riesz transforms on generalized Heisenberg groups and Riesz transforms associated to the CCR heat flow. (English) Zbl 1061.43013

Lust-Piquard, Françoise

Publ. Mat., Barc. 48, No. 2, 309-333 (2004).

Inspired by a method of 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 \(H\).

Reviewer: Khristo N. Boyadzhiev (Ada)

MSC:

43A80	Analysis on other specific Lie groups
46L60	Applications of selfadjoint operator algebras to physics
46L57	Derivations, dissipations and positive semigroups in \(C^*\)-algebras

Keywords:

heat operator; Riesz transform; \(H\)-groups

Citations:

Zbl 0645.60061