Boundedness of functions in fractional Orlicz–Sobolev spaces

A necessary and sufficient condition for fractional Orlicz–Sobolev spaces to be continuously embedded into L∞(Rn) is exhibited. Under the same assumption, any function from relevant fractional-order shown continuous. Improvements of this result are also offered. They provide optimal Orlicz target space, rearrangement-invariant space in embedding question. These results complement those already available subcritical case, where fails. augment a classical theorem standard Sobolev spaces.