Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces

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The Littlewood-Paley theory is extended to weighted spaces of distributions on $[-1,1]$ with Jacobi weights $ \w(t)=(1-t)^α(1+t)^β. $ Almost exponentially localized polynomial elements (needlets) $\{ϕ_ξ\}$, $\{ψ_ξ\}$ are constructed and, in complete analogy with the classical case on $\RR^n$, it is shown that weighted Triebel-Lizorkin and Besov spaces can be characterized by the size of the needlet coefficients $\{\ip{f,ϕ_ξ}\}$ in respective sequence spaces.
34 pages

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Classical Analysis and ODEs, 42A38, 42B08, 42B15

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http://salesiana.dossiersoluciones.com/handle/123456789/118036

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0610624
 http://arxiv.org/abs/math/0610624

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arXiv