Approximation Characteristics of the Spaces $S_p^{ϕ}$ in Different Metrics

Abstract

We continue the investigation of the approximation characteristics of the spaces $S_p^{ϕ}$ introduced earlier. In particular, we establish direct and inverse theorems on the approximation of elements of these spaces. We also determine the exact values of upper bounds of $m$-term approximations of $q$-ellipsoids in the spaces $S_p^{ϕ}$ in the metrics of the spaces $S_p^{ϕ}$.