Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball |
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Authors: | Kyriazis, G. Petrushev, P. Xu, Yuan |
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Affiliation: | Department of Mathematics and Statistics University of Cyprus 1678 Nicosia Cyprus |
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Abstract: | Weighted Triebel–Lizorkin and Besov spaces on the unitball Bd in d with weights wµ(x)=(1–|x|2)µ–1/2,µ0, are introduced and explored. A decomposition schemeis developed in terms of almost exponentially localized polynomialelements (needlets) {}, {} and it is shown that the membershipof a distribution to the weighted Triebel–Lizorkin orBesov spaces can be determined by the size of the needlet coefficients{f, } in appropriate sequence spaces. |
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