Sobolev space on $M \times [0,\infty)$, $M$ compact closed manifold

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Consider a manifold of the form $M \times [0,\infty)$, where $M$ is a closed compact manifold without boundary. So $M \times [0,\infty)$ is a semi-infinite cylinder. I want to know information about Sobolev space on $M \times [0,\infty)$ and basic properties like trace theorems, Poincare type inequalities would be good too.

Is there any nice reference for such domains? I have been searching for days with no luck.