Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness

Abstract

We find two-sides estimates for the best uniform approximations of classes of convolutions of $2\pi$-periodic functions from unit ball of the space $L_p,1\le p<\infty ,$ with fixed kernels, modules of Fourier coefficients of which satisfy the condition $\sum _{k=n+1}^{\infty }\psi (k)<\psi (n).$ In the case of $\sum _{k=n+1}^{\infty }\psi (k)=o(1)\psi (n)$ the obtained estimates become the asymptotic equalities.

19 pages