Logarithmic Sobolev inequalities and contractivity properties of semigroups

The geometry of Markov diffusion generators

“…The equivalence between logarithmic Sobolev inequality and hypercontractivity is an important issue when studying rates of convergence to the equilibrium (cf. [Gr2] and the references therein).…”

Log-Sobolev inequalities for semi-direct product operators and applications

“…Similar inequalities can be proved for some classes of manifolds, both compact and non compact; here we prefer to skip this line of research and refer the reader to the survey [GR2] and the book by F-Y.Wang [Wa1,Example 5.7.2]).…”

Dirichlet boundary conditions for elliptic operators with unbounded drift

“…Let B be the unit ball of H (Ω, µ) is compactly embedded in L 2 (Ω, µ). The fact that T (t) maps L 2 (Ω, µ) into L q(t) (Ω, µ), as well as estimate (13), follow from [5,6].…”