On lower bounds for the widths of classes of functions defined by integral moduli of continuity

Abstract

We establish lower bounds for the Kolmogorov widths d _2n-1(W ^r H ₁ ^ω .L _p ) and Gel’fand widths d ^2n-1(W ^r H ₁ ^ω .L _p ) of the classes of functions W ^r H ₁ ^ω with a convex integral modulus of continuity ω(t).