Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces

George Kyriazis, Pencho Petrushev, and Yuan Xu. "Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces." Studia Mathematica 186.2 (2008): 161-202. <http://eudml.org/doc/284735>.

@article{GeorgeKyriazis2008,
abstract = {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.},
author = {George Kyriazis, Pencho Petrushev, Yuan Xu},
journal = {Studia Mathematica},
keywords = {localized polynomial kernels; Jacobi weight; Triebel-Lizorkin spaces; Besov spaces; frames},
language = {eng},
number = {2},
pages = {161-202},
title = {Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces},
url = {http://eudml.org/doc/284735},
volume = {186},
year = {2008},
}

TY - JOUR
AU - George Kyriazis
AU - Pencho Petrushev
AU - Yuan Xu
TI - Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces
JO - Studia Mathematica
PY - 2008
VL - 186
IS - 2
SP - 161
EP - 202
AB - 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.
LA - eng
KW - localized polynomial kernels; Jacobi weight; Triebel-Lizorkin spaces; Besov spaces; frames
UR - http://eudml.org/doc/284735
ER -