Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

L¹-convergence and hypercontractivity of diffusion semigroups on manifolds

100%

Wang F.-Y.

Studia Mathematica

2004

tom 162

nr 3

219-227

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.

Ograniczanie wyników

1 Studia Mathematica

1 Wang F.-Y.

1 2004

Wyniki wyszukiwania

L¹-convergence and hypercontractivity of diffusion semigroups on manifolds