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## Compactly Supported Frames for Spaces of Distributions in the Framework of Dirichlet Spaces

A 2013 Preprint by S. Dekel, G. Kerkyacharian, G. Kyriazis, and P. Petrushev

• 2013:04
• A small perturbation method is developed and deployed to the construction of compactly supported frames for Besov and Triebel-Lizorkin in the general setting of Dirichlet space with a doubling measure and local scale-invariant Poincaré inequality. This allows, in particular, to develop compactly supported frames for Besov and Triebel-Lizorkin spaces in the context of Lie groups, Riemannian manifolds, and various other settings. The compactly supported frames are utilized for the development of atomic Hardy spaces $H _ {A}^p$ in the general framework of Dirichlet spaces.

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