Hypercontractivity estimates for nonselfadjoint diffusion semigroups
Ross G. Pinsky · Proceedings of the American Mathematical Society · 1988
We use Gross’ results on logarithmic Sobolev inequalities and hypercontractivity to show that the hypercontractivity of a positive recurrent diffusion semigroup depends essentially only on its invariant probability measure and a given diffusion matrix and its diffusion matrix. Thus all diffusion semigroups (including the unique selfadjoint one) with a given invariant probability measure and a given diffusion matrix are essentially equally hypercontractive.