Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces
George Kyriazis ; Pencho Petrushev ; Yuan Xu
Studia Mathematica, Tome 187 (2008), p. 161-202 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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) φξ, ψξ 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,φξ⟩ in respective sequence spaces.

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:284735 
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm186-2-3,
     author = {George Kyriazis and Pencho Petrushev and Yuan Xu},
     title = {Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces},
     journal = {Studia Mathematica},
     volume = {187},
     year = {2008},
     pages = {161-202},
     zbl = {1283.42011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm186-2-3}
}

George Kyriazis; Pencho Petrushev; Yuan Xu. Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces. Studia Mathematica, Tome 187 (2008) pp. 161-202. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm186-2-3/