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:
File | Dimensione | Formato | |
---|---|---|---|
Canale&Tarantino.pdf
accesso aperto
Descrizione: articolo principale
Tipologia:
Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza:
Creative commons
Dimensione
181.2 kB
Formato
Adobe PDF
|
181.2 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.