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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

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.)

Citations:

Zbl 0635.00013
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