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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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
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spelling todo:paper_03733114_v_n_p_Brasco2023-10-03T15:30:21Z A note on homogeneous Sobolev spaces of fractional order Brasco, L. Salort, A. Fractional Sobolev spaces Nonlocal operators Poincaré inequality Real interpolation 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. INPR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03733114_v_n_p_Brasco
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Fractional Sobolev spaces
Nonlocal operators
Poincaré inequality
Real interpolation
spellingShingle Fractional Sobolev spaces
Nonlocal operators
Poincaré inequality
Real interpolation
Brasco, L.
Salort, A.
A note on homogeneous Sobolev spaces of fractional order
topic_facet Fractional Sobolev spaces
Nonlocal operators
Poincaré inequality
Real interpolation
description 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.
format INPR
author Brasco, L.
Salort, A.
author_facet Brasco, L.
Salort, A.
author_sort Brasco, L.
title A note on homogeneous Sobolev spaces of fractional order
title_short A note on homogeneous Sobolev spaces of fractional order
title_full A note on homogeneous Sobolev spaces of fractional order
title_fullStr A note on homogeneous Sobolev spaces of fractional order
title_full_unstemmed A note on homogeneous Sobolev spaces of fractional order
title_sort note on homogeneous sobolev spaces of fractional order
url http://hdl.handle.net/20.500.12110/paper_03733114_v_n_p_Brasco
work_keys_str_mv AT brascol anoteonhomogeneoussobolevspacesoffractionalorder
AT salorta anoteonhomogeneoussobolevspacesoffractionalorder
AT brascol noteonhomogeneoussobolevspacesoffractionalorder
AT salorta noteonhomogeneoussobolevspacesoffractionalorder
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