AverageB-width and infinite-dimensionalG-width of some smooth function classes on the line

The exact values of average σ_B width and infinite dimensional σ_G width of Sobolev class B+r-p(R) in the metric L-p(R)(1≤p≤∞) are obtained and the exact (σ∈N) and strong asymptotic (σ>1) results of infinite_dimensional σ_G width of Sobolev_Wiener class W+r pq(R) in the metric L-q(R) and its dual case_W+r-q(R) in the metric L qp(R)(1≤q≤p≤∞) are achieved.