Hypercontractivity
= Hypercontractivity
{wiki}
A semigroup is hypercontractive when evolution improves integrability through norm bounds $\|P_tf\|_{q(t)}\leq\|f\|_p$ with $q(t)>p$ for positive times. For a symmetric Markov semigroup satisfying a <logarithmic Sobolev inequality> with the joint-energy normalization, one may take $q(t)=1+(p-1)e^{4t/c_{\mathrm{LS}}}$.
// Target: analysis.bigb