Lebesque-type inequalities for the Fourier sums on classes of\n generalized Poisson integrals

2018/04/16 by Serdyuk, Anatoly, Тетяна Степанюк, Stepaniuk, Tetiana
Mathematics · #Mathematical Approximation and Integration #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces

paper · pdf · doi:10.48550/arxiv.1804.05722

Abstract

For functions from the set of generalized Poisson integrals\nC^\α,r_\βL_p, 1\≤ p <\∞, we obtain upper estimates for\nthe deviations of Fourier sums in the uniform metric in terms of the best\napproximations of the generalized derivatives f^\α,r_\β of\nfunctions of this kind by trigonometric polynomials in the metric of the spaces\nL_p. Obtained estimates are asymptotically best possible.\n

Related

• Asymptotically best possible Lebesque-type inequalities for the Fourier sums on sets of generalized Poisson integrals
• Approximations of classes of generalized Poisson integrals by Fourier sums in metrics of spaces L_s
• Approximation by Fourier sums on the classes of generalized Poisson integrals
• Uniform approximations by Fourier sums on classes of generalized Poisson integrals
• Approximation of generalized Poisson integrals by interpolation trigonometric polynomials