Some boundedness properties of certain stationary diffusion semigroups. (English) Zbl 0562.60078
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 E. B. Davies and B. Simon’s, Ultracontractive semigroups and some problems in analysis. To appear in: Aspects of mathematics and its applications, North-Holland.
Reviewer: R.Mikulevičius
MSC:
| 60J35 | Transition functions, generators and resolvents |
| 47D07 | Markov semigroups and applications to diffusion processes |
Keywords:
conservative diffusion semigroup; hypoelliptic smooth diffusion operator; Malliavin calculusReferences:
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