Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces
Date
2008Source
Studia MathematicaVolume
186Issue
2Pages
161-202Google Scholar check
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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) {ρξ}, {ψξ} are constructed and, in complete analogy with the classical case on ℝn, it is shown that weighted Triebel-Lizorkin and Besov spaces can be characterized by the size of the needlet coefficients {(f, ρξ)} in respective sequence spaces. © Instytut Matematyczny PAN, 2008.