PR ] 1 3 Ju l 2 00 4 Interpolated inequalities between exponentialand Gaussian , Orlicz hypercontractivity and isoperimetry

@inproceedings{Barthe2004PR1,
  title={PR ] 1 3 Ju l 2 00 4 Interpolated inequalities between exponentialand Gaussian , Orlicz hypercontractivity and isoperimetry},
  author={F. Barthe and Patrick Cattiaux and Cyril Roberto},
  year={2004}
}
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… CONTINUE READING
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