Journal of Fourier Analysis and Applications

, Volume 22, Issue 6, pp 1416–1430 | Cite as

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

Article

Abstract

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

Keywords

Conical square function Admissibility function Mehler kernel Gaussian measure 

Notes

Acknowledgments

The research has been supported by the Academy of Finland via the Centre of Excellence in Analysis and Dynamics Research (Project No. 271983). The author wishes to thank Alex Amenta and Jonas Teuwen for enlightening discussions.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland

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