On the modulus of continuity of fractional Orlicz-Sobolev functions
Abstract Necessary and sufficient conditions are presented for a fractional Orlicz-Sobolev space on $${\mathbb {R}}^n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:math> 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.
Authors
- Luboš Pick (ORCID: https://orcid.org/0000-0002-3584-1454)
- Angela Alberico (ORCID: https://orcid.org/0000-0001-6364-8531)
- Andrea Cianchi (ORCID: https://orcid.org/0000-0002-1198-8718)
- Lenka Slavíková (ORCID: https://orcid.org/0000-0001-5144-5665)
Institutions
- Charles University (CZ)
- Istituto per le Applicazioni del Calcolo Mauro Picone (IT)
- National Research Council (IT)
- Liceo scientifico statale Ulisse Dini
- University of Florence (IT)
Publication Details
- Journal
- Mathematische Annalen
- Published
- 2024-09-02
- DOI
- https://doi.org/10.1007/s00208-024-02964-z
- Citations
- 3
- Primary Topic
- Nonlinear Partial Differential Equations
- Type
- article
- Field-Weighted Citation Impact
- 2.93
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