An L^1-estimate for certain spectral multipliers associated with the Ornstein--Uhlenbeck operator

Abstract

We study a class of spectral multipliers ϕ(L) for the Ornstein--Uhlenbeck operator L arising from the Gaussian measure on R^n and find a sufficient condition for integrability of ϕ(L)f in terms of the admissible conical square function and a maximal function.

11 pages, revised version, to appear in Journal of Fourier Analysis and Applications

References in corpus (2)

• Non-uniformly local tent spaces
• Finite speed of propagation and off-diagonal bounds for Ornstein-Uhlenbeck operators in infinite dimensions

Cited by in corpus (3)

• The Hardy-Littlewood property and maximal operators associated with the inverse Gauss measure
• Admissible decomposition for spectral multipliers on Gaussian L^p
• Lusin area integrals related to Jacobi expansions