Geodesic
Multivariate Haar systems in Besov function spaces
Sbornik. Mathematics, Tome 212 (2021) no. 6, pp. 810-842

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SM_2021_212_6_a2,
     author = {P. Oswald},
     title = {Multivariate {Haar} systems in {Besov} function spaces},
     journal = {Sbornik. Mathematics},
     pages = {810--842},
     publisher = {mathdoc},
     volume = {212},
     number = {6},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2021_212_6_a2/}
}
TY  - JOUR
AU  - P. Oswald
TI  - Multivariate Haar systems in Besov function spaces
JO  - Sbornik. Mathematics
PY  - 2021
SP  - 810
EP  - 842
VL  - 212
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2021_212_6_a2/
LA  - en
ID  - SM_2021_212_6_a2
ER  - 
%0 Journal Article
%A P. Oswald
%T Multivariate Haar systems in Besov function spaces
%J Sbornik. Mathematics
%D 2021
%P 810-842
%V 212
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2021_212_6_a2/
%G en
%F SM_2021_212_6_a2
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/