• Corpus ID: 246485399

Spectral multipliers in a general Gaussian setting

@inproceedings{Casarino2022SpectralMI,
  title={Spectral multipliers in a general Gaussian setting},
  author={Valentina Casarino and Paolo Ciatti and Peter Sjogren},
  year={2022}
}

• Valentina Casarino, P. Ciatti, P. Sjogren
• Published 3 February 2022
• Mathematics

We investigate a class of spectral multipliers for an Ornstein–Uhlenbeck operator L in R, with drift given by a real matrix B whose eigenvalues have negative real parts. We prove that if m is a function of Laplace transform type defined in the right half-plane, then m(L) is of weak type (1, 1) with respect to the invariant measure in R. The proof involves many estimates of the relevant integral kernels and also a bound for the number of zeros of the time derivative of the Mehler kernel, as well as an enhanced version of the Ornstein–Uhlenbeck maximal operator theorem.