Jacobi decomposition of weighted Triebel–Lizorkin and Besov spaces
Studia Mathematica, Tome 186 (2008) no. 2, pp. 161-202
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
The Littlewood–Paley theory is extended to weighted spaces of
distributions on $[-1,1]$ with Jacobi weights
$w(t)=(1-t)^\alpha(1+t)^\beta.$
Almost exponentially localized polynomial elements (needlets)
$\{\varphi_\xi\}$, $\{\psi_\xi\}$ are constructed
and,
in complete analogy with the classical case on $\mathbb R^n$,
it is shown that weighted Triebel–Lizorkin and Besov spaces
can be characterized by the size of the needlet coefficients
$\{\langle f,\varphi_\xi\rangle\}$
in respective sequence spaces.
Keywords:
littlewood paley theory extended weighted spaces distributions jacobi weights t alpha beta almost exponentially localized polynomial elements needlets varphi psi constructed complete analogy classical mathbb shown weighted triebel lizorkin besov spaces characterized size needlet coefficients langle varphi rangle respective sequence spaces
Affiliations des auteurs :
George Kyriazis 1 ; Pencho Petrushev 2 ; Yuan Xu 3
@article{10_4064_sm186_2_3,
author = {George Kyriazis and Pencho Petrushev and Yuan Xu},
title = {Jacobi decomposition of weighted {Triebel{\textendash}Lizorkin} and {Besov} spaces},
journal = {Studia Mathematica},
pages = {161--202},
publisher = {mathdoc},
volume = {186},
number = {2},
year = {2008},
doi = {10.4064/sm186-2-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm186-2-3/}
}
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 SP - 161 EP - 202 VL - 186 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm186-2-3/ DO - 10.4064/sm186-2-3 LA - en ID - 10_4064_sm186_2_3 ER -
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George Kyriazis; Pencho Petrushev; Yuan Xu. Jacobi decomposition of weighted Triebel–Lizorkin and Besov spaces. Studia Mathematica, Tome 186 (2008) no. 2, pp. 161-202. doi: 10.4064/sm186-2-3
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