Relative infinite-dimensional width of Sobolev classes

In this paper, in order to consider the problems of relative width of Sobolev classes on R in LP, 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.