How do fractional Orlicz-Sobolev spaces relate to each other? This paper characterizes embeddings among these spaces, revealing new results in borderline situations where standard embeddings fail. The study recovers standard embeddings for classical fractional Sobolev spaces while exploring novel results where the latter fall short. The equivalence of Gagliardo-Slobodeckij norms in fractional Orlicz-Sobolev spaces to norms defined via Littlewood-Paley decompositions, oscillations, or Besov type difference quotients is established. This equivalence, of independent interest, is a key tool in the proof of the relevant embeddings. These findings are supported by a new optimal inequality for convolutions in Orlicz spaces.
This article, published in Potential Analysis, contributes to the journal's focus on mathematical analysis and potential theory. By exploring embeddings within fractional Orlicz-Sobolev spaces, it advances our understanding of these complex mathematical structures and their applications in related fields.
| Category | Category Repetition |
|---|---|
| Science: Mathematics | 9 |
| Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods | 2 |