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Article Dans Une Revue Journal of Functional Analysis Année : 2010

Hypercontractivity for log-subharmonic functions

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Résumé

We prove strong hypercontractivity (SHC) inequalities for logarithmically subharmonic functions on R n and different classes of measures: Gaussian measures on R n , symmetric Bernoulli and symmetric uniform probability measures on R , as well as their convolutions. Surprisingly, a slightly weaker strong hypercontractivity property holds for any symmetric measure on R . A log-Sobolev inequality (LSI) is deduced from the (SHC) for compactly supported measures on R n , still for log-subharmonic functions. An analogous (LSI) is proved for Gaussian measures on R n and for other measures for which we know the (SHC) holds. Our log-Sobolev inequality holds in the log-subharmonic category with a constant smaller than the one for Gaussian measure in the classical context.

Dates et versions

hal-03040216 , version 1 (04-12-2020)

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Piotr Graczyk, Todd Kemp, Jean-Jacques Loeb. Hypercontractivity for log-subharmonic functions. Journal of Functional Analysis, 2010, 258 (6), pp.1785 - 1805. ⟨10.1016/j.jfa.2009.08.014⟩. ⟨hal-03040216⟩
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