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Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces

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Kyriazis G., Petrushev P., Xu Y.

Studia Mathematica

2008

tom 186

nr 2

161-202

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.

Ograniczanie wyników

1 Studia Mathematica

1 Kyriazis G.

1 Petrushev P.

1 Xu Y.

1 2008

Wyniki wyszukiwania

Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces