Geodesic
Multivariate Haar systems in Besov function spaces
Sbornik. Mathematics, Tome 212 (2021) no. 6, pp. 810-842 Cet article a éte moissonné depuis la source Math-Net.Ru

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We determine all cases for which the $d$-dimensional Haar wavelet system $H^d$ on the unit cube $I^d$ is a conditional or unconditional Schauder basis in the classical isotropic Besov function spaces ${B}_{p,q,1}^s(I^d)$, $0, $0\le s < 1/p$, defined in terms of first-order $L_p$-moduli of smoothness. We obtain similar results for the tensor-product Haar system $\widetilde{H}^d$, and characterize the parameter range for which the dual of ${B}_{p,q,1}^s(I^d)$ is trivial for $0. Bibliography: 31 titles.
Keywords: Haar system, unconditional convergence
Mots-clés : Besov spaces, Schauder bases in quasi-Banach spaces, piecewise-constant approximation. 
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     title = {Multivariate {Haar} systems in {Besov} function spaces},
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P. Oswald. Multivariate Haar systems in Besov function spaces. Sbornik. Mathematics, Tome 212 (2021) no. 6, pp. 810-842. http://geodesic.mathdoc.fr/item/SM_2021_212_6_a2/

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