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.
- Grand Lebesgue spaces
- Kolmogorov compactness
- Rellich-Kondrachov compactness
- grand Sobolev spaces
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