Decomposition systems for function spaces

• Autorzy: G. Kyriazis
• Języki publikacji: 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.

Kategorie tematyczne

• 41A20: Approximation by rational functions
• 42B25: Maximal functions, Littlewood-Paley theory
• 42C15: General harmonic expansions, frames
• 41A17: Inequalities in approximation (Bernstein, Jackson, Nikol\cprime ski{\u\i}-type inequalities)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 157
• Numer: 2
• Strony: 133-169

Daty

wydano

2003

Twórcy

autor

G. Kyriazis

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

Identyfikatory

DOI

10.4064/sm157-2-3