On the pre-compactness of a set in the generalized Morrey spaces

In this paper, we present sufficient conditions for the pre-compactness of sets in the generalized Morrey spaces Mpw. From this theorem for the case of w(r) = r-λ follows the known result for the Morrey space Mpλ, and in the case of λ = 0 this is the well-known Frechet-Kolmogorov theorem. © 2016 Author(s).