Sur les transformations de Riesz pour le semi-groupe d’Ornstein- Uhlenbeck. (Riesz’s transformation on the Ornstein-Uhlenbeck process). (French) Zbl 0606.60063

Gundy, Richard F.

C. R. Acad. Sci., Paris, Sér. I 303, 967-970 (1986).

In this note the author presents a proof of the Riesz inequalities for the infinite dimensional Ornstein-Uhlenbeck semi-group of Malliavin. The inequalities in this setting were first proved by P. A. Meyer [see e.g., Lect. Notes Math. 1059, 179-193 (1984; Zbl 0543.60078)]. The present proof uses a scheme first employed by the author and N. Th. Varopoulos to give a probabilistic interpretation to the classical Riesz inequalities [C. R. Acad. Sci., Paris Sér. A 289, 13-16 (1979; Zbl 0413.60003)].

MSC:

60H99	Stochastic analysis
60J60	Diffusion processes

Keywords:

Riesz inequalities; infinite dimensional Ornstein-Uhlenbeck semi-group