On the maximal operator of a general Ornstein–Uhlenbeck semigroup
Journal article, 2022

If Q is a real, symmetric and positive definite n× n matrix, and B a real n× n matrix whose eigenvalues have negative real parts, we consider the Ornstein–Uhlenbeck semigroup on Rn with covariance Q and drift matrix B. Our main result says 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.

Mehler kernel

Gaussian measure

Weak type (1,1)

Maximal operator

Ornstein–Uhlenbeck semigroup

Author

VALENTINA CASARINO

University of Padua

PAOLO CIATTI

University of Padua

Peter Sjögren

University of Gothenburg

Chalmers, Mathematical Sciences

Mathematische Zeitschrift

0025-5874 (ISSN) 1432-8232 (eISSN)

Vol. In Press

Subject Categories

Algebra and Logic

Computational Mathematics

Mathematical Analysis

DOI

10.1007/s00209-022-02986-w

More information

Latest update

3/14/2022