Widths and average widths of Sobolev classes

This paper concerns the problem of the Kolmogorov n-width, the linear n-width, the Gel'fand n-width and the Bernstein n-width of Sobolev classes of the periodic multivariate functions in the space L-p(T-d) and the average Bernstein sigma-width, average Kolmogorov sigma-widths, the average linear sigma-widths of Sobolev classes of the multivariate functions in the space L-p(R-d), where p = (p(i),...,p(d)), 1 less than or equal to p(j) < infinity, j = 1, 2,...,d, or p(j) = infinity, j = 1, 2,...,d. Their weak asymptotic behaviors are established for the corresponding quantities.