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• # Artykuł - szczegóły

## Studia Mathematica

2003 | 157 | 2 | 133-169

## Decomposition systems for function spaces

EN

### Abstrakty

EN
Let $Θ: = {θ_{I}^{e}: e ∈ E, I ∈ D}$ be a decomposition system for $L₂(ℝ^{d})$ indexed over D, the set of dyadic cubes in $ℝ^{d}$, and a finite set E, and let $Θ̃: = {Θ̃ _{I}^{e}: e ∈ E, I ∈ D}$ be the corresponding dual functionals. That is, for every $f ∈ L₂(ℝ^{d})$, $f = ∑_{e∈E} ∑_{I∈D} ⟨f,Θ̃_{I}^{e}⟩ θ_{I}^{e}$. 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 $⟨f,Θ̃_{I}^{e}⟩$, e ∈ E, I ∈ D. Typical examples of such decomposition systems are various wavelet-type unconditional bases for $L₂(ℝ^{d})$, and more general systems such as affine frames.

133-169

wydano
2003

### Twórcy

autor
• Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus