Geodesic
Approximation of Polynomials in the Haar System in Weighted Symmetric Spaces
Matematičeskie zametki, Tome 99 (2016) no. 5, pp. 649-657

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For weighted symmetric (or rearrangement-invariant) spaces with nontrivial Boyd indices and weights from suitable Muckenhoupt classes, the basis property of the Haar system in these spaces and two versions of the direct theorem on the approximation by polynomials in the Haar system are established.
Keywords: approximation by polynomials in the Haar system, weighted symmetric space, basis property of the Haar system, Muckenhoupt class, Hölder's inequality, generalized modulus of continuity, Banach function space. 
@article{MZM_2016_99_5_a1,
     author = {S. S. Volosivets},
     title = {Approximation of {Polynomials} in the {Haar} {System} in {Weighted} {Symmetric} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {649--657},
     publisher = {mathdoc},
     volume = {99},
     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_5_a1/}
}
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S. S. Volosivets. Approximation of Polynomials in the Haar System in Weighted Symmetric Spaces. Matematičeskie zametki, Tome 99 (2016) no. 5, pp. 649-657. http://geodesic.mathdoc.fr/item/MZM_2016_99_5_a1/