Some boundedness properties of certain stationary diffusion semigroups (Q1056998)

Let \((P_ t)\) be some conservative diffusion semigroup with uniformly hypoelliptic smooth diffusion operator and let m be a \((P_ t)\)- invariant probability measure on \(R^ N\). Using Malliavin calculus the authors estimate \(\| P_ t\|_{L^ p(m)\to L^ q(m)}(1<p<q\leq \infty,t>0)\). They explain what advantages their results have in comparison to \textit{E. B. Davies} and \textit{B. Simon's}, Ultracontractive semigroups and some problems in analysis. To appear in: Aspects of mathematics and its applications, North-Holland.