Average widths and optimal recovery of multivariate Besov classes inL p (Rd)

Some weak asymptotic results for average δ -K width and average δ -L width of the isotropic Besov classes S^r _p6B(R ^d), S^r _p6b(R^d), and the aniwtropic Besov classes S^r _p0B(R^d),. S^r _p6b(R^d), 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 S^r _p0B(R ^d), inL _p (R^d) (1≤p≤∞).