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EnglishThe paper deals with the operator $u \rightarrow gu$ defined in the Sobolev space $W^{r,p}(\Omega)$ and which takes values in $L^p(\Omega)$ when $\Omega$ is an unbounded open subset in $R^n$. The functions $g$ belong to Morrey type spaces which provide an intermediate space between $L ^\infty(\Omega)$ and $L^p_{loc}(\Omega)$ . The main result is an embedding result from which we can deduce a Fefferman type inequality. $L^p$ estimates and a compactness result are also stated.
| Titolo: | Embedding and compactness results for multiplication operators in Sobolev spaces |
| Autori: | |
| Data di pubblicazione: | 2014 |
| Abstract: | The paper deals with the operator $u \rightarrow gu$ defined in the Sobolev space $W^{r,p}(\Omega)$ and which takes values in $L^p(\Omega)$ when $\Omega$ is an unbounded open subset in $R^n$. The functions $g$ belong to Morrey type spaces which provide an intermediate space between $L ^\infty(\Omega)$ and $L^p_{loc}(\Omega)$ . The main result is an embedding result from which we can deduce a Fefferman type inequality. $L^p$ estimates and a compactness result are also stated. |
| Handle: | http://hdl.handle.net/11386/4526265 |
| ISBN: | 978-88-6887-003-4 |
| Appare nelle tipologie: | 2.1.2 Articolo su libro con ISBN |
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