On the maximal operator of a general Ornstein-Uhlenbeck semigroup

• If Q is a real, symmetric and positive definite n x n matrix, and B a real n x n 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 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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Nyckelord

Ornstein-Uhlenbeck semigroup

Maximal operator

Gaussian measure

Mehler

kernel

Weak type (1

1)

Mathematics

Mehler kernel

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