Sufficient conditions for the pre-compactness of sets in global Morrey-type spaces

In this paper we give sufficient conditions for the precompactness of sets in general global Morrey-type spaces GMpθ,w(·)(ℝn). In the case θ = ∞, it follows the result for the generalized Morrey spaces Mp w, and for w(r) = r-λ, θ = ∞, 0≤λ≤np there follows the known result for the Morrey spaces Mpλ(ℝn). In the case λ = 0 this is the well-known Frechet-Kolmogorov theorem. The pre-compactness of sets in Morrey spaces was investigated in many works, and in generalized Morrey spaces Mp w(ℝn) in our previous works. The aim of this paper is to generalize these results to the case of general global Morrey-type spaces GMpθ,w(·)(ℝn). © 2017 Author(s).