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Hypercontractivity for Markov Semigroups (2101.01616v2)
Published 5 Jan 2021 in math.FA and math.PR
Abstract: We investigate in a systematic way hypercontractivity property in Orlicz spaces for Markov semi-groups related to homogeneous and non homogeneous diffusions in $\mathbb{R}{n}$. 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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