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Weyl calculus with respect to the Gaussian measure and Lp-Lq boundedness of the Ornstein-Uhlenbeck semigroup in complex time

Date: Thursday, June 01, 2017 16:00 - 18:00
Speaker: Jan van Neerven (TU Delft)
Location: Seminar room Big Ground floor / Office Bldg West (I21.EG.101)
Series: Formal Sciences Seminar
Host: Jan Maas
Lab building west seminar room

Abstract:

We introduce a Weyl functional calculus for the Ornstein-Uhlenbeck operator L=−Δ+x⋅∇, and give a simple criterion for Lp-Lq boundedness of operators in this functional calculus. It allows us to recover, unify, and extend, old and new results concerning the boundedness of exp(−zL)as an operator from Lp(ℝdα) to Lq(ℝdβ) for suitable values of z∈ℂ with ℜz>0 and α,β>0. Here, γτ denotes the centred Gaussian measure on ℝd with density (2πτ)−d/2 exp(−|x|2/2τ).

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