Riesz meets Sobolev

• Autorzy: Thierry Coulhon , Adam Sikora
• Języki publikacji: EN

Abstrakty

EN

We show that the $L^{p}$ boundedness, p > 2, of the Riesz transform on a complete non-compact Riemannian manifold with upper and lower Gaussian heat kernel estimates is equivalent to a certain form of Sobolev inequality. We also characterize in such terms the heat kernel gradient upper estimate on manifolds with polynomial growth.

Kategorie tematyczne

• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)
• 58J35: Heat and other parabolic equation methods

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 118
• Numer: 2
• Strony: 685-704

Daty

wydano

2010

Twórcy

autor

Thierry Coulhon

• Département de Mathématiques, Université de Cergy-Pontoise, Site de Saint-Martin, 2, rue Adolphe Chauvin, F-95302 Cergy-Pontoise Cedex, France

autor

Adam Sikora

• Department of Mathematics, Macquarie University, Sydney, NSW 2109, Australia

Identyfikatory

DOI

10.4064/cm118-2-20