Decomposition systems for function spaces
G. Kyriazis
Studia Mathematica, Tome 157 (2003), p. 133-169 / Harvested from The Polish Digital Mathematics Library

Let Θ:=θIe:eE,ID be a decomposition system for L(d) indexed over D, the set of dyadic cubes in d, and a finite set E, and let Θ̃:=Θ̃Ie:eE,ID be the corresponding dual functionals. That is, for every fL(d), f=eEIDf,Θ̃IeθIe. We study sufficient conditions on Θ,Θ̃ so that they constitute a decomposition system for Triebel-Lizorkin and Besov spaces. Moreover, these conditions allow us to characterize the membership of a distribution f in these spaces by the size of the coefficients f,Θ̃Ie, e ∈ E, I ∈ D. Typical examples of such decomposition systems are various wavelet-type unconditional bases for L(d), and more general systems such as affine frames.

Publié le : 2003-01-01
EUDML-ID : urn:eudml:doc:285306
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G. Kyriazis. Decomposition systems for function spaces. Studia Mathematica, Tome 157 (2003) pp. 133-169. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm157-2-3/