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 M p w . From this theorem for the case of w(r) = r −λ follows the known result for the Morrey space M p λ , and in the case of λ = 0 this is the well-known Frechet-Kolmogorov theorem.