On the maximal operator of a general Ornstein–Uhlenbeck semigroup
Artikel i vetenskaplig tidskrift, 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

Författare

VALENTINA CASARINO

Università di Padova

PAOLO CIATTI

Università di Padova

Peter Sjögren

Göteborgs universitet

Chalmers, Matematiska vetenskaper

Mathematische Zeitschrift

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

Vol. In Press

Ämneskategorier

Algebra och logik

Beräkningsmatematik

Matematisk analys

DOI

10.1007/s00209-022-02986-w

Mer information

Senast uppdaterat

2022-03-14