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.
1)
weak type $(1
Ornstein--Uhlenbeck semigroup
Mehler kernel
Gaussian measure
Riesz transforms
Author
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 135Roots
Basic sciences
Subject Categories
Mathematical Analysis
DOI
10.1007/s00526-021-01988-6