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

In this paper, we consider some classes of 2π-periodic convolution functions , and 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 , in the space L ^p for 1 < p < ∞. Project supported by the Natural Science Foundation of China (Grant No. 10671019), Research Fund for the Doctoral Program Higher Education (No. 20050027007) and Scientific Research Fund of Zhejiang Provincial Education Department (No. 20070509)