Herbst inequalities for supercontractive semigroups
The authors consider symmetric Markov semigroups \((e^{-tA})_{t\geq 0}\) on \(L^{2}(X,\mu)\) and the corresponding Dirichlet form \(E(f,f)=\| A^{1 \over 2}f\| _{2}^{2}\). If \(\| e^{-tA}\| _{p \to q} < \infty\) for \(1<p,q<\infty\), i.e., the semigroup is supercontractive, they derive exponential integrability inequalities, called Herbst inequalities.
scientific article; zbMATH DE number 1251227