Bernstein n-widths for classes of convolution functions with kernels satisfying certain oscillation properties

In this paper, we consider some classes of 2.-periodic convolution functions B~p, and K~p with kernels having certain oscillation properties, which include the classical Sobolev class as special case. With the help of the spectral of nonlinear integral equations, we determine the exact values of Bernstein n-width of the classes B~p, K~p in the space L p for 1 < p < ..