Semigroups of operators and function spaces on Lie groups.

DOI10.1016/0021-9045(91)90101-FzbMath0745.47030MaRDI QIDQ1177065

Laurent Saloff-Coste, Thierry Coulhon

Publication date: 25 June 1992

Published in: Journal of Approximation Theory (Search for Journal in Brave)

zbMATH Keywords

imbedding theoremsHerz-Bernstein Theorem on the Wiener algebraleft invariant sub-laplacians on unimodular Lie groupsLipschitz, Besov, and Sobolev spacessymmetric sub-markovian semi-groups

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Markov semigroups and applications to diffusion processes (47D07) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15)

Related Items

Sobolev algebras on Lie groups and noncommutative geometry, Gagliardo-Nirenberg inequalities for semigroups of operators and applications, Heat kernel generated frames in the setting of Dirichlet spaces, Besov class via heat semigroup on Dirichlet spaces. I: Sobolev type inequalities, Riesz potentials and amalgams

Cites Work

• Analyse sur les groupes de Lie à croissance polynômiale. (Analysis on Lie groups of polynomial growth)
• Harmonic analysis on semigroups
• Analysis on nilpotent groups
• Hardy-Littlewood theory for semigroups
• Besov spaces and Sobolev spaces on a nilpotent Lie group
• An Endpoint Estimate for Certain k-Plane Transforms
• Lipschitz classes and Poisson integrals on stratified groups
• Croissance polynomiale et périodes des fonctions harmoniques
• On a theorem of functional analysis
• Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)
• Analysis on Lie groups
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