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arXiv · 2004.04022

Riesz transforms of a general Ornstein--Uhlenbeck semigroup

Valentina Casarino·Paolo Ciatti·Peter Sjögren
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Abstract

We consider Riesz transforms of any order associated to an Ornstein--Uhlenbeck operator $\mathcal L$, 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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Valentina Casarino, Paolo Ciatti, Peter Sjögren. 2020-04-08. Riesz transforms of a general Ornstein--Uhlenbeck semigroup. https://doi.org/10.1007/s00526-021-01988-6

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