Fractional Orlicz-Sobolev embeddings into Campanato type spaces

Abstract

Optimal embeddings for fractional Orlicz-Sobolev spaces into (generalized) Campanato spaces on the Euclidean space are exhibited. Embeddings into vanishing Campanato spaces are also characterized. Sharp embeddings into $\mathrm{BMO}({\mathbb{R}}^n)$ and $\mathrm{VMO}({\mathbb{R}}^n)$ are derived as special instances. Dissimilarities to corresponding embeddings for classical fractional Sobolev spaces are pointed out.