Nonlocal Poincaré inequalities on Lie groups with polynomial volume growth and Riemannian manifolds

• Autorzy: Emmanuel Russ , Yannick Sire
• Języki publikacji: EN

Abstrakty

EN

Let G be a real connected Lie group with polynomial volume growth endowed with its Haar measuredx. Given a C² positive bounded integrable function M on G, we give a sufficient condition for an L² Poincaré inequality with respect to the measure M(x)dx to hold on G. We then establish a nonlocal Poincaré inequality on G with respect to M(x)dx. We also give analogous Poincaré inequalities on Riemannian manifolds and deal with the case of Hardy inequalities.

Kategorie tematyczne

• 42B35: Function spaces arising in harmonic analysis
• 26D10: Inequalities involving derivatives and differential and integral operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 203
• Numer: 2
• Strony: 105-127

Daty

wydano

2011

Twórcy

autor

Emmanuel Russ

• Université Paul Cézanne, LATP, Faculté des Sciences et Techniques, Case cour A, Avenue Escadrille Normandie-Niemen, F-13397 Marseille Cedex 20, France
• CNRS, LATP, CMI, 39 rue F. Joliot-Curie, F-13453 Marseille Cedex 13, France

autor

Yannick Sire

• Université Paul Cézanne, LATP, Faculté des Sciences et Techniques, Case cour A, Avenue Escadrille Normandie-Niemen, F-13397 Marseille Cedex 20, France
• CNRS, LATP, CMI, 39 rue F. Joliot-Curie, F-13453 Marseille Cedex 13, France

Identyfikatory

DOI

10.4064/sm203-2-1