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. 
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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/

[1] C. Bennett, R. Sharpley, Interpolation of Operators, Pure Appl. Math., 129, Academic Press, Boston, MA, 1988 | MR | Zbl

[2] B. Muckenhoupt, “Weighted norm inequalities for the Hardy maximal function”, Trans. Amer. Math. Soc., 165 (1972), 207–226 | DOI | MR | Zbl

[3] B. C. Kashin, A. A. Saakyan, Ortogonalnye ryady, Izd-vo AFTs, M., 1999 | MR | Zbl

[4] I. I. Sharapudinov, “Priblizhenie funktsii iz prostranstv Lebega i Soboleva s peremennym pokazatelem summami Fure–Khaara”, Matem. sb., 205:2 (2014), 145–160 | DOI | MR | Zbl

[5] A. S. Krantsberg, “O bazisnosti sistemy Khaara v vesovykh prostranstvakh”, Tr. Mosk. in-ta elektron. mashinostr., 24 (1972), 14–26

[6] D. W. Boyd, “Spaces between a pair of reflexive Lebesgue spaces”, Proc. Amer. Math. Soc., 18 (1967), 215–219 | DOI | MR | Zbl

[7] A. Yu. Karlovich, “On the essential norm of the Cauchy singular operator in weighted rearrangement-invariant spaces”, Integral Equations Operator Theory, 38:1 (2000), 28–50 | DOI | MR | Zbl

[8] A. Yu. Karlovich, “Fredholmness of singular integral operators with piecewise continuous coefficients on weighted Banach function spaces”, J. Integral Equations Appl., 15:3 (2003), 263–320 | DOI | MR | Zbl

[9] A. Böttcher, Yu. I. Karlovich, Carleson Curves, Muckenhoupt Weights and Toeplitz Operators, Progr. Math., 154, Birkhäuser Verlag, Basel, 1997 | MR | Zbl

[10] A. Yu. Karlovich, “Algebras of singular integral operators with PC coeffcients in rearrangement-invariant spaces with Muckenhoupt weights”, J. Operator Theory, 47:2 (2002), 303–323 | MR | Zbl

[11] W. S. Young, “Weighted norm inequalities for Vilenkin–Fourier series”, Trans. Amer. Math. Soc., 340:1 (1993), 273–291 | DOI | MR | Zbl