1Department of Mathematics and Statistics University of Cyprus 1678 Nicosia, Cyprus 2Department of Mathematics University of South Carolina Columbia, SC 29208, U.S.A. and Institute of Mathematics and Informatics Bulgarian Academy of Sciences 3Department of Mathematics University of Oregon Eugene, OR 97403, U.S.A.
Studia Mathematica, Tome 186 (2008) no. 2, pp. 161-202
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.
1
Department of Mathematics and Statistics University of Cyprus 1678 Nicosia, Cyprus
2
Department of Mathematics University of South Carolina Columbia, SC 29208, U.S.A. and Institute of Mathematics and Informatics Bulgarian Academy of Sciences
3
Department of Mathematics University of Oregon Eugene, OR 97403, U.S.A.
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author = {George Kyriazis and Pencho Petrushev and Yuan Xu},
title = {Jacobi decomposition of weighted {Triebel{\textendash}Lizorkin} and {Besov} spaces},
journal = {Studia Mathematica},
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language = {en},
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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
