The paper deals with the operator $u ightarrow gu$ 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.
Embedding and compactness results for multiplication operators in Sobolev spaces
CANALE, Anna;TARANTINO, CIRO
2014
Abstract
The paper deals with the operator $u ightarrow gu$ 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.File in questo prodotto:
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