Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces   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) $\{\phi_\xi\}$,
$\{\psi_\xi\}$ are constructed and, in complete analogy with the classical case
on $\RR^n$, it is shown that weighted Triebel-Lizorkin and Besov spaces can be
characterized by the size of the needlet coefficients $\{\ip{f,\phi_\xi}\}$ in
respective sequence spaces.

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The categories of this paper are: eess
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The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
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The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th