Consider a normal Ornstein-Uhlenbeck semigroup in Euclidean space, whose covariance is given by a positive definite matrix. The drift matrix is assumed to have eigenvalues only in the left half-plane. We prove that the associated maximal operator is of weak type (1, 1) with respect to the invariant measure. This extends earlier work by G. Mauceri and L. Noselli. The proof goes via the special case where the matrix defining the covariance is I and the drift matrix is diagonal.
The maximal operator of a normal Ornstein-Uhlenbeck semigroup is of weak type (1,1)
CASARINO, VALENTINA;CIATTI, PAOLO;
2020
Abstract
Consider a normal Ornstein-Uhlenbeck semigroup in Euclidean space, whose covariance is given by a positive definite matrix. The drift matrix is assumed to have eigenvalues only in the left half-plane. We prove that the associated maximal operator is of weak type (1, 1) with respect to the invariant measure. This extends earlier work by G. Mauceri and L. Noselli. The proof goes via the special case where the matrix defining the covariance is I and the drift matrix is diagonal.
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