Hypercontractivity for Markov semi-groups
Journal of Functional Analysis(2022)
Abstract
We investigate in a systematic way hypercontractivity property in Orlicz spaces for Markov semi-groups related to homogeneous and non homogeneous diffusions in Rn. We provide an explicit construction of a family of Orlicz functions for which we prove that the associated hypercontractivity property is equivalent to a suitable functional inequality.
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Key words
Hypercontractivity,Ornstein-Uhlenbeck semigroup,Markov semi-groups,Γ2 calculus
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