Some ss-numbers of embeddings in function spaces with polynomial weights

In this paper, we investigate the asymptotic behavior of the Gelfand, Kolmogorov and Weyl numbers of Sobolev embeddings in weighted function spaces of Besov and Triebel–Lizorkin type with polynomial weights. The exact estimates for the Gelfand and Kolmogorov numbers are obtained in the so-called non-limiting case and complement those previous results in the quasi-Banach setting. Also, the asymptotic order of the Weyl numbers is established by means of the basic Weyl estimates in the finite-dimensional spaces improved recently as well as flexible uses of the operator ideal technique.