We consider Riesz transforms of any order associated to an Ornstein--Uhlenbeck operator , with covariance Q given by a real, symmetric and positive definite matrix, and with drift B 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.
Riesz transforms of a general Ornstein--Uhlenbeck semigroup
Valentina Casarino;Paolo Ciatti;Peter Sjögren
2021
Abstract
We consider Riesz transforms of any order associated to an Ornstein--Uhlenbeck operator , with covariance Q given by a real, symmetric and positive definite matrix, and with drift B 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.
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