Seminar
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Analysis and Probability Seminar

Peter Sjögren, Chalmers/University of Gothenburg: Variation inequalities for the Ornstein-Uhlenbeck semigroup

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Overview

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  • Date:Starts 12 March 2024, 13:15Ends 12 March 2024, 14:15
  • Location:
    MV:L14, Chalmers tvärgata 3
  • Language:English

Abstract: We consider the Ornstein-Uhlenbeck semigroup Ht, t>0, in dimension one. It is known that Ht f -> f as t -> 0, in Lp and almost everywhere.

To measure the speed of convergence, one introduces the variation seminorm, taken with respect to t. This notion has been studied in many different contexts.

We show that this seminorm for Ht defines an operator of weak type (1,1) with respect to the relevant Gaussian measure. The analogous Lp estimates for 1 < p < ∞ were already known.

Jakob Björnberg
  • Head of Unit, Analysis and Probability Theory, Mathematical Sciences
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