Sharp bounds for composition with quasiconformal mappings in Sobolev spaces
Let φ be a quasiconformal mapping, and let Tφ be the composition operator which maps f to f ˝ φ. Since φ may not be bi-Lipschitz, the composition operator need not map Sobolev spaces to themselves. The study begins with the behavior of Tφ on Lp and W1,p for 1 ă p ă 8. This cases are well understood...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:287737 |
| Acceso en línea: | https://ddd.uab.cat/record/287737 https://dx.doi.org/urn:doi:10.1016/j.jmaa.2017.02.016 |
| Access Level: | acceso abierto |
| Palabra clave: | Sobolev spaces Fractional smoothness Quasiconformal mappings Composition operator |
| Sumario: | Let φ be a quasiconformal mapping, and let Tφ be the composition operator which maps f to f ˝ φ. Since φ may not be bi-Lipschitz, the composition operator need not map Sobolev spaces to themselves. The study begins with the behavior of Tφ on Lp and W1,p for 1 ă p ă 8. This cases are well understood but alternative proofs of some known results are provided. Using interpolation techniques it is seen that compactly supported Bessel potential functions in Hs,p are sent to Hs,q whenever 0 ă s ă 1 for appropriate values of q. The techniques used lead to sharp results and they can be applied to Besov spaces as well. |
|---|