Author:
Alberico Angela,Cianchi Andrea,Pick Luboš,Slavíková Lenka
Abstract
AbstractNecessary 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.
Funder
Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni
Ministero dell’Università e della Ricerca
Grantová Agentura Ceské Republiky
Grantová Agentura, Univerzita Karlova
Università degli Studi di Firenze
Publisher
Springer Science and Business Media LLC
Reference37 articles.
1. Alberico, A., Cianchi, A., Pick, L., Slavíková, L.: On the limit as $$s\rightarrow 0^+$$ of fractional Orlicz-Sobolev spaces. J. Fourier Anal. Appl. 26(6), 80 (2020)
2. Alberico, A., Cianchi, A., Pick, L., Slavíková, L.: On the limit as $$s\rightarrow 1^-$$ of possibly non-separable fractional Orlicz-Sobolev spaces. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 31, 879–899 (2020)
3. Alberico, A., Cianchi, A., Pick, L., Slavíková, L.: Fractional Orlicz-Sobolev embeddings. J. Math. Pures Appl. 149, 216–253 (2021)
4. Alberico, A., Cianchi, A., Pick, L., Slavíková, L.: On fractional Orlicz-Sobolev spaces. Anal. Math. Phys. 11(84), 21 (2021)
5. Alberico, A., Cianchi, A., Pick, L., Slavíková, L.: Boundedness of functions in fractional Orlicz-Sobolev spaces. Nonlinear Anal. 230, 113–231 (2023)