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Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry.

Franck BarthePatrick CattiauxCyril Roberto — 2006

Revista Matemática Iberoamericana

We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general F-Sobolev inequalities, thus extending Gross hypercontractivity theory. We provide criteria for these Sobolev type inequalities and for related properties. In particular, we implement in the context of probability measures the ideas of Maz'ja's capacity theory, and present equivalent forms relating the capacity of sets to their measure. Orlicz hypercontractivity efficiently describes the...

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