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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Jacobi decomposition of weighted Triebel–Lizorkin and Besov spaces

### Tom 186 / 2008

Studia Mathematica 186 (2008), 161-202 MSC: 42A38, 42B08, 42B15. DOI: 10.4064/sm186-2-3

#### Streszczenie

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.

#### Autorzy

• George KyriazisDepartment of Mathematics and Statistics
University of Cyprus
1678 Nicosia, Cyprus
e-mail
• Pencho PetrushevDepartment of Mathematics
University of South Carolina
Columbia, SC 29208, U.S.A.
and
Institute of Mathematics and Informatics