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Abstract:

We consider a homogeneous fractional Sobolev space obtained by completion of the space of smooth test functions, with respect to a Sobolev–Slobodeckiĭ norm. We compare it to the fractional Sobolev space obtained by the K-method in real interpolation theory. We show that the two spaces do not always coincide and give some sufficient conditions on the open sets for this to happen. We also highlight some unnatural behaviors of the interpolation space. The treatment is as self-contained as possible. © 2019, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature.

Registro:

Documento: Artículo
Título:A note on homogeneous Sobolev spaces of fractional order
Autor:Brasco, L.; Salort, A.
Filiación:Dipartimento di Matematica e Informatica, Università degli Studi di Ferrara, Via Machiavelli 35, Ferrara, 44121, Italy
Departamento de Matemática, FCEN Universidad de Buenos Aires and IMAS, CONICET, Buenos Aires, Argentina
Palabras clave:Fractional Sobolev spaces; Nonlocal operators; Poincaré inequality; Real interpolation
Año:2019
DOI: http://dx.doi.org/10.1007/s10231-018-0817-x
Título revista:Annali di Matematica Pura ed Applicata
Título revista abreviado:Ann. Mat. Pura Appl.
ISSN:03733114
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_03733114_v_n_p_Brasco

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Citas:

---------- APA ----------
Brasco, L. & Salort, A. (2019) . A note on homogeneous Sobolev spaces of fractional order. Annali di Matematica Pura ed Applicata.
http://dx.doi.org/10.1007/s10231-018-0817-x
---------- CHICAGO ----------
Brasco, L., Salort, A. "A note on homogeneous Sobolev spaces of fractional order" . Annali di Matematica Pura ed Applicata (2019).
http://dx.doi.org/10.1007/s10231-018-0817-x
---------- MLA ----------
Brasco, L., Salort, A. "A note on homogeneous Sobolev spaces of fractional order" . Annali di Matematica Pura ed Applicata, 2019.
http://dx.doi.org/10.1007/s10231-018-0817-x
---------- VANCOUVER ----------
Brasco, L., Salort, A. A note on homogeneous Sobolev spaces of fractional order. Ann. Mat. Pura Appl. 2019.
http://dx.doi.org/10.1007/s10231-018-0817-x