Average widths and optimal recovery of multivariate Besov classes in L_p(R~d)

Some weak asymptotic results for average δ -K width and average δ -L width of the isotropic Besov classes Sr p6B(R d), Sr p6b(Rd), and the aniwtropic Besov classes Sr p0B(Rd),. Sr p6b(Rd), inL p(R d) (l p < ∞) are obtained, and the corresponding weak asymptotic optimal subspaces are identified. Furthermore, the weak asymptotic behavior of optimal recovery is established for the isotropic Besov classes Sr p0B(R d), inL p (Rd) (1≤p≤∞).