Relative infinite-dimensional width of Sobolev classes

In this paper, in order to consider the problems of relative width of Sobolev classes W p r on R in L P , we propose the definition of relative infinite-dimensional width which combines the ideas of the relative width and the infinite-dimensional width. We determine the exact values of relative infinite-dimensional width for r = 1 , p = 1 or p = ∞ and for r ∈ N , p = 2 .