Average widths of anisotropic Besov-Wiener classes. (Q1585603)

In a recent paper [Chin. Sci. Bull. 43, No. 8, 479--482 (1998)] the author studied the average width of Besov classes on \({\mathbb R}^d\). In this paper, he continues his investigation and obtains the weak asymptotic behavior of average \(\sigma-K\) width and average \(\sigma-L\) width for some anisotropic Besov-Wiener classes \(S^r_{pq\theta}({\mathbb R}^d)\) and \(S^r_{pq\theta}({\mathbb R}^d)\) \((1\leq q\leq p<\infty)\). Weakly asymptotic optimal subspaces of average dimension \(\leq\sigma\) (\(\sigma\geq 1\)) are also obtained.