Basis property of the Legendre polynomials in variable exponent Lebesgue spaces

被引：0

作者：

Magomed-Kasumov, M. G. ^{[1
,2
]}

Shakh-Emirov, T. N. ^{[1
]}

Gadzhimirzaev, R. M. ^{[1
]}

机构：

[1] Russian Acad Sci, Daghestan Fed Res Ctr, Makhachkala, Russia

[2] Russian Acad Sci, Vladikavkaz Sci Ctr, Vladikavkaz, Russia

来源：

SBORNIK MATHEMATICS | 2024年 / 215卷 / 02期

关键词：

Lebesgue space; variable exponent; Legendre polynomials; basis; the Dini-Lipschitz condition;

D O I：

10.4213/sm9891e

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Sharapudinov proved that the Legendre polynomials form a basis of the Lebesgue space with variable exponent p(x) if p(x) > 1 satisfies the Dini-Lipschitz condition and is constant near the endpoints of the orthogonality interval. We prove that the system of Legendre polynomials forms a basis of these spaces without the condition that the variable exponent be constant near the endpoints. Bibliography: 9 titles.

引用

页码：234 / 249

页数：16

共 50 条

[1] Basis Property of the Haar System in Weighted Lebesgue Spaces with Variable Exponent
Magomed-Kasumov, M. G.
MATHEMATICAL NOTES, 2024, 115 (5-6) : 755 - 763
[2] The Basis Property of Ultraspherical Jacobi Polynomials in a Weighted Lebesgue Space with Variable Exponent
I. I. Sharapudinov
Mathematical Notes, 2019, 106 : 616 - 638
[3] The Basis Property of Ultraspherical Jacobi Polynomials in a Weighted Lebesgue Space with Variable Exponent
Sharapudinov, I. I.
MATHEMATICAL NOTES, 2019, 106 (3-4) : 616 - 638
[4] The basis property of the Legendre polynomials in the variable exponent Lebesgue space L>p(x)(-1,1)
Sharapudinov, I. I.
SBORNIK MATHEMATICS, 2009, 200 (1-2) : 133 - 156
[5] A criterion for the basis property of perturbed exponential systems in Lebesgue spaces with variable exponent
Bilalov, B. T.
Guseinov, Z. G.
DOKLADY MATHEMATICS, 2011, 83 (01) : 93 - 96
[6] A criterion for the basis property of perturbed exponential systems in Lebesgue spaces with variable exponent
B. T. Bilalov
Z. G. Guseinov
Doklady Mathematics, 2011, 83 : 93 - 96
[7] Approximation by Haar polynomials in variable exponent grand Lebesgue spaces
Volosivets, S. S.
APPLICABLE ANALYSIS, 2024, 103 (08) : 1447 - 1458
[8] Approximation by Haar and Walsh Polynomials in Weighted Variable Exponent Lebesgue Spaces
Volosivets, S. S.
RESULTS IN MATHEMATICS, 2022, 77 (04)
[9] Approximation by trigonometric polynomials in the framework of variable exponent grand Lebesgue spaces
Danelia, Nina
Kokilashvili, Vakhtang
GEORGIAN MATHEMATICAL JOURNAL, 2016, 23 (01) : 43 - 53
[10] Approximation by Haar and Walsh Polynomials in Weighted Variable Exponent Lebesgue Spaces
S. S. Volosivets
Results in Mathematics, 2022, 77

← 1 2 3 4 5 →