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.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
Casarino-Ciatti-Sjogren-Riesz-ArXiv.pdf
accesso aperto
Descrizione: MIUR (PRIN 2016 “Real and Complex Manifolds: Geometry, Topology and Harmonic Analysis”). The third author was supported by GNAMPA (Professore Visitatore Bando 30/11/2018).
Tipologia:
Preprint (submitted version)
Licenza:
Accesso gratuito
Dimensione
335.56 kB
Formato
Adobe PDF
|
335.56 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
