Approximation of the classes of convolutions of periodic functions by Zygmund sums in integral metrics - Grabova, U. Z. (Reports of the National Academy of Sciences of Ukraine, 2014)
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.