Lebesque-type inequalities for the Fourier sums on classes of generalized Poisson integrals
Abstract
For functions from the set of generalized Poisson integrals Cα,rβLp, 1≤ p <∞, we obtain upper estimates for the deviations of Fourier sums in the uniform metric in terms of the best approximations of the generalized derivatives fα,rβ of functions of this kind by trigonometric polynomials in the metric of the spaces Lp. Obtained estimates are asymptotically best possible.
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