If Q is a real, symmetric and positive definite nxn matrix, and B a real nxn matrix whose eigenvalues have negative real parts, we consider the Ornstein--Uhlenbeck semigroup on R^n with covariance Q and drift matrix B. Our main result is that the associated maximal operator is of weak type (1,1) with respect to the invariant measure. The proof has a geometric gist and hinges on the ``forbidden zones method'' previously introduced by the third author. For large values of the time parameter, we also prove a refinement of this result, in the spirit of a conjecture due to Talagrand.

On the maximal operator of a general Ornstein--Uhlenbeck semigroup

Casarino V.
;
Ciatti P.;SJOGREN, STEN OLOF PETER
2022

Abstract

If Q is a real, symmetric and positive definite nxn matrix, and B a real nxn matrix whose eigenvalues have negative real parts, we consider the Ornstein--Uhlenbeck semigroup on R^n with covariance Q and drift matrix B. Our main result is that the associated maximal operator is of weak type (1,1) with respect to the invariant measure. The proof has a geometric gist and hinges on the ``forbidden zones method'' previously introduced by the third author. For large values of the time parameter, we also prove a refinement of this result, in the spirit of a conjecture due to Talagrand.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3286177
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