Are dualizing modules stable under localization Let $(R,m,k)$ be a (noetherian) regular local ring of depth=dimension $d$, and let $D$ be a dualizing module for $R$ (say, the injective envelope of $R/m$).  
Then is $D_p$ dualizing for $R_p$ for any prime $p$ of $R$ (more generally, if $R$ is Gorenstein and $p$ is a prime such that $R_p$ is also Gorenstein)?  If it is true, could I have a reference for a proof?
Bump!

I hope by dualizing module you mean canonical module. Please check page no 110 theorem 3.3.5 of the book Cohen Macaulay ring by Bruns and Herzog. Please do inform me if you have still difficulties.
