Maz’ya–Shaposhnikova formula in magnetic fractional Orlicz–Sobolev spaces

Article type: Research Article

Authors: Maione, Alberto^{a; *} | Salort, Ariel M.^{b; c} | Vecchi, Eugenio^d

Affiliations: [a] Abteilung für Angewandte Mathematik, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 10, 79104 Freiburg i. Br., Germany. E-mail: [email protected] | [b] Departamento de Matemática, FCEyN – Universidad de Buenos Aires, Pabellón I (1428) Av. Cantilo s/n., Buenos Aires, Argentina. E-mail: [email protected]; URL: http://mate.dm.uba.ar/~asalort | [c] IMAS – CONICET Ciudad Universitaria, Argentina | [d] Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 20133, Milano (MI), Italy. E-mail: [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: In this note we prove the validity of the Maz’ya–Shaposhnikova formula in magnetic fractional Orlicz–Sobolev spaces. This complements a previous asymptotic study performed by the second author in (Studia Mathematica (2020)).

Keywords: Asymptotic behaviours, Orlicz spaces, fractional Sobolev norms

DOI: 10.3233/ASY-211677

Journal: Asymptotic Analysis, vol. 126, no. 3-4, pp. 201-214, 2022