Fractional Orlicz-Sobolev embeddings

The optimal Orlicz target space and the optimal rearrangement- invariant target space are exhibited for embeddings of fractional-order Orlicz- Sobolev spaces W^{s,A}(R^n). Related Hardy type inequalities are proposed as well. Versions for fractional Orlicz-Sobolev seminorms of the Bourgain-Brezis-Mironescu theorem on the limit as s->1^- and of the Maz'ya-Shaposhnikova theorem on the limit as s ->0^+ are established. This is a joint work with Andrea Cianchi, Lubos Pick and Lenka Slavikova.