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Approximation of functions and their conjugates in Lp and uniform metric by Euler means

Volosivets S. S., Tyuleneva A. A.

Demonstratio Mathematica

2018

Vol. 51, nr 1

141--150

For 2π-periodic functions from Lp (where 1 < p < ∞) we prove an estimate of approximation by Euler means in Lp metric generalizing a result of L. Rempuska and K. Tomczak. Furthermore, we show that this estimate is sharp in a certain sense. We study the uniform approximation of functions by Euler means in terms of their best approximations in p-variational metric and also prove the sharpness of this estimate under some conditions. Similar problems are treated for conjugate functions.