Super Logarithmic Sobolev inequalities and Nash-type inequalities for sub-markovian symmetric semigroups
Résumé
We study relationships between Logarithmic Sobolev inequalities with one parameter of Davies-Simon type, energy-entropy inequality, Nash-type inequality and Sobolev-type inequalities. The inequalities of Sobolev-type apply in the general setting of symmetric sub-Markovian semigroups (and some generalizations). We provide several examples of application of theses results for ultracontractive semigroups but also for some non-ultracontractive like Ornstein-Ulhenbeck semigroup.
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