Morrey type spaces and multiplication operator in Sobolev spaces

Abstract

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.