Morrey type spaces and multiplication operator in Sobolev spaces

The paper deals with the operator $u\rightarrow gu$ defined in the Sobolev space $W^{r,p}(Ω)$ and which takes values in $L^p(Ω)$ when $Ω$ is an unbounded open subset in $R^n$. The functions $g$ belong to wider spaces of $L^p$ connected with the Morrey type spaces. $L^p$ estimates and compactness results are stated.

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