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

S. Dekel ¹   ; G. Kerkyacharian ²   ; G. Kyriazis ³   ; P. Petrushev ⁴

¹ Hamanofim St. 9 Herzelia, Israel
² Laboratoire de Probabilités et Modèles Aléatoires CNRS-UMR 7599 Université Paris VI et Université Paris VII rue de Clisson F-75013 Paris, France
³ Department of Mathematics and Statistics University of Cyprus 1678 Nicosia, Cyprus
⁴ Department of Mathematics University of South Carolina Columbia, SC 29208, U.S.A.

Studia Mathematica, Tome 225 (2014) no. 2, pp. 115-163

Résumé

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.

Détail

DOI : 10.4064/sm225-2-2

Keywords: small perturbation method developed employed construct frames compactly supported elements small shrinking support besov triebel lizorkin spaces general setting doubling metric measure space presence nonnegative self adjoint operator whose heat kernel has gaussian localization markov property allows particular construct compactly supported frames besov triebel lizorkin spaces sphere interval jacobi weights lie groups riemannian manifolds various other settings compactly supported frames utilized introduce atomic hardy spaces general setting article