On the variation operator for the Ornstein-Uhlenbeck semigroup in higher dimension
Seminari di Analisi Matematica dell'Università e del Politecnico di Torino
Date: Wednesday, 29 November 2023 14:30 - 15:30
Venue: Peter Sjögren - Aula Buzano (DISMA Politecnico di Torino)
In joint work with V. Casarino and P. Ciatti, we study the variation seminorm of a general Ornstein-Uhlenbeck semigroup (Ht)t>0 in Rn, taken with respect to t. It is known that this seminorm defines an operator which is bounded on the L p spaces defined by means of the invariant Gaussian measure, for 1 < p < ∞. We show that one also has the weak type (1,1) here. In an earlier paper, we proved this in the one-dimensional case. But in n dimensions, it requires a different approach. In particular, one uses vectorvalued Calderón-Zygmund techniques for the local part of the variation in the interval 0 < t ≤ 1.
Speaker
Peter Sjögren
Affiliation
University of Gothenburg
Room
Aula Buzano
Proposed by
Alessio Martini e Maria Vallarino
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