Subcritical and Supercritical Fractional Orlicz-Sobolev Embedding

The optimal Orlicz target space and the optimal rearrangement- invariant target space are exhibited for embeddings of fractional-order Orlicz-Sobolev spaces. Both the subcritical and the supercritical regimes are considered. In particular, in the latter case the relevant Orlicz-Sobolev spaces are shown to be embedded into the space of bounded continuous functions in R^n. This is a joint work with Andrea Cianchi, Lubos Pick and Lenka Slavikova.