Year: 2024
Type: article
Abstract: Necessary and sufficient conditions are presented for a fractional Orlicz-Sobolev space on $${\mathbb {R}}^n$$ R n to be continuously embedded into a space of uniformly continuous functions. The optimal modulus of continuity is exhibited whenever these conditions are fulfilled. These results pertain to the supercritical Sobolev regime and complement earlier sharp embeddings into rearrangement-invariant spaces concerning the subcritical setting. Classical embeddings for fractional Sobolev spaces into Hölder spaces are recovered as special instances. Proofs require novel strategies, since customary methods fail to produce optimal conclusions.
Source: Mathematische Annalen
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
Funders: Univerzita Karlova v Praze, Grantová Agentura, Univerzita Karlova, Istituto Nazionale di Alta Matematica "Francesco Severi", Grantová Agentura České Republiky, Ministero dell’Istruzione, dell’Università e della Ricerca, Università degli Studi di Firenze, Ministero dell'Università e della Ricerca, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
OpenAlex ID: W4402135850