# 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} }

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…

## One Citation

### Littlewood-Paley functions associated with general Ornstein-Uhlenbeck semigroups

- Mathematics
- 2022

. In this paper we establish L p ( R d ,γ ∞ )-boundedness properties for square functions involving time and spatial derivatives of Ornstein-Uhlenbeck semigroups. Here γ ∞ denotes the invariant…

## References

SHOWING 1-10 OF 30 REFERENCES

### Spectral multipliers for the Ornstein-Uhlenbeck semigroup

- Mathematics
- 1999

The setting of this paper is Euclidean space with the Gaussian measure. We letL be the associated Laplacian, by means of which the Ornstein-Uhlenbeck semigroup is defined. The main result is a…

### The maximal operator of a normal Ornstein-Uhlenbeck semigroup is of weak type (1,1)

- MathematicsANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
- 2020

Consider a normal Ornstein--Uhlenbeck semigroup in Rn,
whose covariance is given by a positive definite matrix.
The drift matrix is assumed to have eigenvalues only in the left half-plane.
We…

### Riesz transforms of a general Ornstein–Uhlenbeck semigroup

- MathematicsCalculus of Variations and Partial Differential Equations
- 2021

We consider Riesz transforms of any order associated to an Ornstein–Uhlenbeck operator with covariance given by a real, symmetric and positive definite matrix, and with drift given by a real matrix…

### Functional calculus for the Laguerre operator

- Mathematics
- 2005

Abstract.In this paper we study the boundedness of spectral multipliers associated to the multidimensional Laguerre operator . It is well known that, for special values of α, the analysis of the…

### Banach space operators with a bounded H∞ functional calculus

- MathematicsJournal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
- 1996

Abstract In this paper, we give a general definition for f(T) when T is a linear operator acting in a Banach space, whose spectrum lies within some sector, and which satisfies certain resolvent…

### Higher-order Riesz operators for the Ornstein–Uhlenbeck Semigroup

- Mathematics
- 1999

We prove that the second-order Riesz transforms associated to the Ornstein–Uhlenbeck semigroup are weak type (1,1) with respect to the Gaussian measure in finite dimension. We also show that they are…

### Spectrum of Ornstein-Uhlenbeck Operators in Lp Spaces with Respect to Invariant Measures

- Mathematics
- 2002

Abstract Let A =∑ i , j =1 N q ij D ij +∑ i , j =1 N b ij x j D i be a possibly degenerate Ornstein–Uhlenbeck operator in R N and assume that the associated Markov semigroup has an invariant measure…

### Sharp exponential inequalities for the Ornstein-Uhlenbeck operator

- MathematicsJournal of Functional Analysis
- 2021

### Maximal operator, Littlewood-Paley functions and variation operators associated with nonsymmetric Ornstein-Uhlenbeck operators

- Mathematics
- 2022

In this paper we establish L boundedness properties for maximal operators, Littlewood-Paley functions and variation operators involving Poisson semigroups and resolvent operators associated with…

### The Sector of Analyticity of the Ornstein–Uhlenbeck Semigroup on Lp Spaces with Respect to Invariant Measure

- Mathematics
- 2003

The sector of analyticity of the Ornstein–Uhlenbeck semigroup is computed on the space Lμp := Lp (RN; μ) with respect to its invariant measure μ. If A=Δ + Bx· ∇ denotes the generator of the…