Pisier, Gilles Riesz transforms: A simpler analytic proof of P. A. Meyer’s inequality. (English) Zbl 0645.60061 Séminaire de probabilités XXII, Strasbourg/France, Lect. Notes Math. 1321, 485-501 (1988). [For the entire collection see Zbl 0635.00013.] The author gives an analytical proof of P. A. Meyer’s inequality \[ C_ p^{-1}\| L^{1/2}f\|_ p\leq \| \nabla f\|_ p\leq C_ p\| L^{1/2}f\|_ p,\quad 1<p<\infty, \] where L is the generator of an Ornstein-Uhlenbeck process: \(L=A-(x\), \(\nabla)\). All the norms are relative to the canonical Gauss measure on \({\mathbb{R}}^ n \)and the constant \(C_ p\) is independent of n. Both P. A. Meyers original proof and the latter simpler proof of Gundy are probabilistic. Reviewer: Murali Rao Cited in 3 ReviewsCited in 37 Documents MSC: 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60J60 Diffusion processes 60E15 Inequalities; stochastic orderings 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) Keywords:Riesz transforms; Hermite polynomials; Ornstein-Uhlenbeck process; Gauss measure Citations:Zbl 0635.00013 PDFBibTeX XML Full Text: Numdam EuDML