Riesz transforms of a general Ornstein-Uhlenbeck semigroup
Journal article, 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 whose eigenvalues have negative real parts. In this general Gaussian context, we prove that a Riesz transform is of weak type (1,1) with respect to the invariant measure if and only if its order is at most 2.


weak type $(1

Ornstein--Uhlenbeck semigroup

Mehler kernel

Gaussian measure

Riesz transforms


Valentina Casarino

University of Padua

Paolo Ciatti

University of Padua

Peter Sjögren

Chalmers, Mathematical Sciences

Calculus of Variations and Partial Differential Equations

0944-2669 (ISSN) 1432-0835 (eISSN)

Vol. 60 4 135


Basic sciences

Subject Categories

Mathematical Analysis



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