Compactly supported frames for spaces of distributions associated with nonnegative self-adjoint operators

• Autorzy: S. Dekel , G. Kerkyacharian , G. Kyriazis , P. Petrushev
• Języki publikacji: EN

Abstrakty

EN

A small perturbation method is developed and employed to construct frames with compactly supported elements of small shrinking support for Besov and Triebel-Lizorkin spaces in the general setting of a doubling metric measure space in the presence of a nonnegative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. This allows one, in particular, to construct compactly supported frames for Besov and Triebel-Lizorkin spaces on the sphere, on the interval with Jacobi weights as well as on Lie groups, Riemannian manifolds, and in various other settings. The compactly supported frames are utilized to introduce atomic Hardy spaces $H^{p}_{A}$ in the general setting of this article.

Kategorie tematyczne

• 42C15: General harmonic expansions, frames
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 58J35: Heat and other parabolic equation methods

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 225
• Numer: 2
• Strony: 115-163

Daty

wydano

2014

Twórcy

autor

S. Dekel

• Hamanofim St. 9, Herzelia, Israel

autor

G. Kerkyacharian

• Laboratoire de Probabilités et Modèles Aléatoires, CNRS-UMR 7599, Université Paris VI et Université Paris VII, rue de Clisson, F-75013 Paris, France

autor

G. Kyriazis

• Department of Mathematics and Statistics, University of Cyprus, 1678 Nicosia, Cyprus

autor

P. Petrushev

• Department of Mathematics, University of South Carolina, Columbia, SC 29208, U.S.A.

Identyfikatory

DOI

10.4064/sm225-2-2