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

For 2π-periodic functions from L p (where 1 < p < ∞) we prove an estimate of approximation by Euler means in L p 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.

Abstract licence: CC BY-NC-ND

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