Fractional Laplacian, homogeneous Sobolev spaces and their realizations

We study the fractional Laplacian and the homogeneous Sobolev spaces on R d , by considering two definitions that are both considered classical. We compare these different definitions, and show how they are related by providing an explicit correspondence between these two spaces, and show that they...

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Bibliographic Details
Published in:Annali di matematica pura ed applicata 2020-12, Vol.199 (6), p.2243-2261
Main Authors: Monguzzi, Alessandro, Peloso, Marco M., Salvatori, Maura
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Sobolev space
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Summary:We study the fractional Laplacian and the homogeneous Sobolev spaces on R d , by considering two definitions that are both considered classical. We compare these different definitions, and show how they are related by providing an explicit correspondence between these two spaces, and show that they admit the same representation. Along the way, we also prove some properties of the fractional Laplacian.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-020-00966-7