AVERAGE B-WIDTH AND INFINITEDIMENSIONAL G-WIDTH OF SOMESMOOTH FUNCTION CLASSES ON THE LINE

摘要

In this paper, we get the exact values of average σ-B width and infinite dimensional σ-G width of Sobolev class Bp (R) in the metric Lp (R) (1≤p≤∞) and obtain the exact (σ∈N) and strong asymptotic (σ>1 ) results of infinite dimensional σ-G widths of Sobolev-Wiener class WrM (R) in the metric Lq(R) and its dual case Wrp(R) in the metric Lqp(R) (1≤q≤p≤∞)