Fractional Gagliardo–Nirenberg interpolation inequality and bounded mean oscillation

Jean Van Schaftingen

doi:10.5802/crmath.463

Analyse fonctionnelle, Analyse harmonique

Fractional Gagliardo–Nirenberg interpolation inequality and bounded mean oscillation

Jean Van Schaftingen ¹

¹ Université catholique de Louvain, Institut de Recherche en Mathématique et Physique, Chemin du Cyclotron 2 bte L7.01.01, 1348 Louvain-la-Neuve, Belgium

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1041-1049.

Résumé

We prove Gagliardo–Nirenberg interpolation inequalities estimating the Sobolev semi-norm in terms of the bounded mean oscillation semi-norm and of a Sobolev semi-norm, with some of the Sobolev semi-norms having fractional order.

Reçu le : 2023-01-03
Accepté le : 2023-01-06
Publié le : 2023-09-07

DOI : 10.5802/crmath.463

Classification : 26D10, 35A23, 42B35, 46B70, 46E35

Affiliations des auteurs :

Jean Van Schaftingen ¹

¹ Université catholique de Louvain, Institut de Recherche en Mathématique et Physique, Chemin du Cyclotron 2 bte L7.01.01, 1348 Louvain-la-Neuve, Belgium

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Jean Van Schaftingen},
     title = {Fractional {Gagliardo{\textendash}Nirenberg} interpolation inequality and bounded mean oscillation},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1041--1049},
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     year = {2023},
     doi = {10.5802/crmath.463},
     language = {en},
}

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Jean Van Schaftingen. Fractional Gagliardo–Nirenberg interpolation inequality and bounded mean oscillation. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1041-1049. doi : 10.5802/crmath.463. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.463/

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