Average B-width and infinite dimensional G-width of some smooth function classes on the line

摘要

In this paper, we get the exact values of averageσ-B width and infinite dimensionalσ-G width of Sobolev class B~r_p(R)in the metric L_p(R)(1≤p≤∞)and obtain the exact(σ∈N)and strong asymptotic(σ>1)results of infinite dimensionalσ-G widths of Sobolev-Wiener class W~r_pq (R)in the metric L_q(R)and its dual case W~r_p(R)in the metric L_pq(R)(1≤q≤p≤∞　).