On fractional Orlicz–Sobolev spaces

Abstract Some recent results on the theory of fractional Orlicz–Sobolev spaces are surveyed. They concern Sobolev type embeddings for these with an optimal Orlicz target, related Hardy inequalities, and criteria compact embeddings. The limits when smoothness parameter $$s\in (0,1)$$ s ? ( 0 , 1 ) tends to either endpoints its range also discussed. This note is based papers ours, where additional material proofs can be found.