Lebesgue inequalities for poisson integrals

被引：0

作者：

Stepanets A.I. ^{[1
]}

Serdyuk A.S. ^{[1
]}

机构：

[1] Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

来源：

Ukrainian Mathematical Journal | 2000年 / 52卷 / 6期

关键词：

Trigonometric Polynomial; Poisson Kernel; Poisson Integral; Finite Norm; Good Uniform Approximation;

D O I：

10.1007/BF02591785

中图分类号：

学科分类号：

摘要：

We obtain estimates for the deviations of the Fourier partial sums on the sets of the Poisson integrals of functions from the space Lp, p ≥ 1, that are expressed in terms of the values of the best approximations of such functions by trigonometric polynomials in the metric of Lp. We show that the estimates obtained are unimprovable on some important functional subsets. © 2000 Kluwer Academic/Plenum Publishers.

引用

页码：914 / 925

页数：11

共 5 条

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[2]

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[3]

Nikol'skii S.M., Approximation of functions by trigonometric polynomials in the mean, Izv. Akad. Nauk SSSR, Ser. Mat., 10, 3, pp. 207-256, (1946)

[4]

Stechkin S.B., Estimate of the remainder of Fourier series for differentiable functions, Trudy Mat. Inst. Akad. Nauk SSSR, 145, pp. 126-151, (1980)

[5]

Stepanets A.I., Classification and Approximation of Periodic Functions [in Russian], (1987)

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