Approximation of the classes of convolutions of periodic functions by Zygmund sums in integral metrics
DOI:
https://doi.org/10.15407/dopovidi2014.09.013Keywords:
classes of convolutions, Zygmund sumsAbstract
We obtain the estimates exact in order for the deviations of Zygmund sums in the metrics of spaces Lq, 1<q<∞, on the classes of 2π-periodic functions that admit a representation in the form of a convolution of functions that belong to a unit ball of the space L1 with fixed kernel Ψβ. We show that, at certain values of the parameters that define the class Lψβ,1 and a method of approximation, the Zygmund sums provide the order of the best approximation of the given classes by trigonometric polynomials in the metric Lq.
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