The Littlewood-Paley theory is extended to weighted spaces of distributions on [-1,1] with Jacobi weights $w\left(t\right)={(1-t)}^{\alpha }{(1+t)}^{\beta }$. Almost exponentially localized polynomial elements (needlets) ${\phi }_{\xi }$, ${\psi }_{\xi }$ 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 $⟨f,{\phi }_{\xi }⟩$ in respective sequence spaces.