Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces

• Autorzy: George Kyriazis , Pencho Petrushev , Yuan Xu
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42B15: Multipliers
• 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
• 42B08: Summability

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 186
• Numer: 2
• Strony: 161-202

Daty

wydano

2008

Twórcy

autor

George Kyriazis

• Department of Mathematics and Statistics, University of Cyprus, 1678 Nicosia, Cyprus

autor

Pencho Petrushev

• Department of Mathematics, University of South Carolina, Columbia, SC 29208, U.S.A.
• Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

autor

Yuan Xu

• Department of Mathematics, University of Oregon, Eugene, OR 97403, U.S.A.

Identyfikatory

DOI

10.4064/sm186-2-3