Characterisation of homogeneous fractional Sobolev spaces
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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad Autónoma de Madrid |
| Repositorio: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.uam.es:10486/705386 |
| Acceso en línea: | http://hdl.handle.net/10486/705386 https://dx.doi.org/10.1007/s00526-021-01934-6 |
| Access Level: | acceso abierto |
| Palabra clave: | 46E35 Fractional Laplacian Fractional P-Laplacian Matemáticas |
| Sumario: | 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 |
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