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arXiv · 1705.00833

The maximal operator of a normal Ornstein--Uhlenbeck semigroup is of weak type $(1,1)$

Valentina Casarino·Paolo Ciatti·Peter Sjögren
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Abstract

Consider a normal Ornstein--Uhlenbeck semigroup in $\Bbb{R}^n$, 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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Valentina Casarino, Paolo Ciatti, Peter Sjögren. 2017-05-02. The maximal operator of a normal Ornstein--Uhlenbeck semigroup is of weak type $(1,1)$. https://doi.org/10.2422/2036-2145.201805_012

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