On entropy numbers and nonlinear approximation by sets of finite pseudo-dimension (Q5930018)

The author announces asymptotic orders of the entropy number \(\varepsilon_n(W,X)\) and the non-linear \(n\)-width \(\varrho_n(W,X)\) when \(X\) is the space \(L_q(\mathbb{T}^d)\) and \(W\) is either the unit ball of the Besov space \(B^r_{p,\theta}\) or the unit ball of the Sobolev space \(W^r_p\). Detailed proofs are missing.