Journal article
Characterisation of homogeneous fractional Sobolev spaces
- Abstract:
- Our aim is to characterize the homogeneous fractional Sobolev–Slobodeckiĭ spaces Ds,p(Rn) and their embeddings, for s∈ (0 , 1] and p≥ 1. They are defined as the completion of the set of smooth and compactly supported test functions with respect to the Gagliardo–Slobodeckiĭ seminorms. For sp<n or s= p= n= 1 we show that Ds,p(Rn) is isomorphic to a suitable function space, whereas for sp≥n it is isomorphic to a space of equivalence classes of functions, differing by an additive constant. As one of our main tools, we present a Morrey–Campanato inequality where the Gagliardo–Slobodeckiĭ seminorm controls from above a suitable Campanato seminorm.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, 524.7KB, Terms of use)
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- Publisher copy:
- 10.1007/s00526-021-01934-6
Authors
- Publisher:
- Springer
- Journal:
- Calculus of Variations and Partial Differential Equations More from this journal
- Volume:
- 60
- Issue:
- 2
- Article number:
- 60
- Publication date:
- 2021-03-03
- Acceptance date:
- 2021-02-05
- DOI:
- EISSN:
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1432-0835
- ISSN:
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0944-2669
Terms of use
- Copyright holder:
- L Brasco et al.
- Copyright date:
- 2021
- Rights statement:
- © The Author(s) 2021. Open Access: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
- Licence:
- CC Attribution (CC BY)
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