On widths of one class of periodic functions

Abstract

In the paper, we have found the A.N. Kolmogorov's width of the class $W^r L^+_p$ ($r=1,2,\ldots$, $1 \leqslant p \leqslant \infty$) of all $2\pi$-periodic functions $f(x)$ whose $(r-1)$-th derivative $f^{(r-1)}(x)$ is absolutely continuous and $\| f^{(r)}_+ \|_p \leqslant 1$.