L¹-convergence and hypercontractivity of diffusion semigroups on manifolds

• Autorzy: Feng-Yu Wang
• Języki publikacji: EN

Abstrakty

EN

Let $P_{t}$ be the Markov semigroup generated by a weighted Laplace operator on a Riemannian manifold, with μ an invariant probability measure. If the curvature associated with the generator is bounded below, then the exponential convergence of $P_{t}$ in L¹(μ) implies its hypercontractivity. Consequently, under this curvature condition L¹-convergence is a property stronger than hypercontractivity but weaker than ultracontractivity. Two examples are presented to show that in general, however, L¹-convergence and hypercontractivity are incomparable.

Kategorie tematyczne

• 47D07: Markov semigroups and applications to diffusion processes
• 60J60: Diffusion processes

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 162
• Numer: 3
• Strony: 219-227

Daty

wydano

2004

Twórcy

autor

Feng-Yu Wang

• Department of Mathematics, Beijing Normal University, Beijing 100875, P.R. China

Identyfikatory

DOI

10.4064/sm162-3-3