An $$L^1$$ L 1 -Estimate for Certain Spectral Multipliers Associated with the Ornstein–Uhlenbeck Operator

Abstract

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