Asymptotically best possible Lebesque-type inequalities for the Fourier sums on sets of generalized Poisson integrals

2019/08/26 by Serdyuk, Anatoly, Stepaniuk, Tetiana
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1908.09517

Abstract

In this paper we establish Lebesgue-type inequalities for 2π-periodic functions f, which are defined by generalized Poisson integrals of the functions φ from L_p, 1≤ p< ∞. In these inequalities uniform norms of deviations of Fourier sums ‖ f-S_n-1 ‖_C are expressed via best approximations E_n(φ)_L_p of functions φ by trigonometric polynomials in the metric of space L_p. We show that obtained estimates are asymptotically best possible.

Related

• Lebesque-type inequalities for the Fourier sums on classes of\n generalized Poisson integrals
• Uniform approximations by Fourier sums on classes of generalized Poisson integrals
• Uniform approximations by Fourier sums on the sets of convolutions of periodic functions of high smoothness
• Approximations of classes of generalized Poisson integrals by Fourier sums in metrics of spaces L_s
• Approximation of generalized Poisson integrals by interpolation trigonometric polynomials