The paper deals with the multiplication operator 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 $L^{\infty}$ and $L^{p}_{loc}(\Omega)$. The main result is a 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

TARANTINO, CIRO
2014

Abstract

The paper deals with the multiplication operator 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 $L^{\infty}$ and $L^{p}_{loc}(\Omega)$. The main result is a embedding result from which we can deduce a Fefferman type inequality. $L^{p}$ estimates and a compactness result are also stated.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/592409
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