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Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces

George KyriazisPencho PetrushevYuan Xu — 2008

Studia Mathematica

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 ℝⁿ, it is shown that weighted Triebel-Lizorkin and Besov spaces can be characterized by the size of the needlet coefficients f , φ ξ in respective sequence spaces.

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