A note on homogeneous Sobolev spaces of fractional order

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...

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Detalles Bibliográficos
Autores principales: Brasco, L., Salort, A.
Formato: INPR
Materias:
Fractional Sobolev spaces
Nonlocal operators
Poincaré inequality
Real interpolation
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03733114_v_n_p_Brasco
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario: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.

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