The relative nn-widths of Sobolev classes with restrictions

We consider relative widths characterizing the best approximation of a fixed set by its sections of given dimension. For Sobolev classes Wp1 on [0,1][0,1] with restriction f(0)=0f(0)=0, we determine the exact orders of such widths in the spaces LqLq for 1≤q≤p≤∞1≤q≤p≤∞. We also obtain the exact values of the corresponding relative widths for p=q=1,1≤q≤p=2p=q=1,1≤q≤p=2 and p=q=∞p=q=∞.