Let be a decomposition system for indexed over D, the set of dyadic cubes in , and a finite set E, and let be the corresponding dual functionals. That is, for every , . 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 , e ∈ E, I ∈ D. Typical examples of such decomposition systems are various wavelet-type unconditional bases for , and more general systems such as affine frames.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm157-2-3, author = {G. Kyriazis}, title = {Decomposition systems for function spaces}, journal = {Studia Mathematica}, volume = {157}, year = {2003}, pages = {133-169}, zbl = {1050.42027}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm157-2-3} }
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/