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The Littlewood-Paley theory is extended to weighted spaces of distributions on [-1,1] with Jacobi weights . Almost exponentially localized polynomial elements (needlets) , 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 in respective sequence spaces.
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