A supersolutions perspective on hypercontractivity

Yosuke Aoki, Jonathan Bennett, Neal Bez, Shuji Machihara, Kosuke Matsuura, Shobu Shiraki

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Abstract

The purpose of this article is to expose an algebraic closure property of supersolutions to certain diffusion equations. This closure property quickly gives rise to a monotone quantity which generates a hypercontractivity inequality. Our abstract argument applies to a general Markov semigroup whose generator is a diffusion and satisfies a curvature condition.
Original languageEnglish
JournalAnnali di Matematica Pura ed Applicata
Volume199
Publication statusPublished - 18 Feb 2020

Bibliographical note

7 pages

Keywords

  • math.FA
  • math.AP
  • math.PR

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