On the compactness in grand spaces

Abstract

Abstract In this paper we study compactness of subsets of grand Lebesgue spaces (also known as Iwaniec–Sbordone spaces) and grand Sobolev spaces. Namely, we prove a Kolmogorov–Riesz compactness theorem for grand Lebesgue spaces and the corresponding version of a result of Sudakov. In addition, the validity of a Rellich–Kondrachov type compact embedding is shown to hold in the context of grand Sobolev spaces.