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

### Tom 225 / 2014

Studia Mathematica 225 (2014), 115-163 MSC: Primary 58J35, 46E35; Secondary 42C15. DOI: 10.4064/sm225-2-2

#### Streszczenie

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.

#### Autorzy

• S. DekelHamanofim St. 9
Herzelia, Israel
e-mail
• G. KerkyacharianLaboratoire de Probabilités et Modèles Aléatoires
CNRS-UMR 7599
Université Paris VI et Université Paris VII
rue de Clisson
F-75013 Paris, France
e-mail
• G. KyriazisDepartment of Mathematics and Statistics
University of Cyprus
1678 Nicosia, Cyprus
e-mail
• P. PetrushevDepartment of Mathematics
University of South Carolina
Columbia, SC 29208, U.S.A.
e-mail

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