Friends, I've never used \part{} before, so bear with me. =)
Consider the following code:
\documentclass[twoside]{book}
\usepackage{lipsum}
\begin{document}
\pagestyle{empty}
\begin{titlepage}
My title page.
\end{titlepage}
\cleardoublepage
\pagestyle{plain}
\frontmatter
\tableofcontents
\clearpage
\mainmatter
\part{Hello World}
\chapter{Test one}
\lipsum[1]
\section{My section one}
\lipsum[1]
\part{Goodbye World}
\chapter{Test two}
\lipsum[1]
\section{My section two}
\lipsum[1]
\end{document}
I'd like to have page numbers in the even pages right after the Part x titles. It would be pages 6 and 10 of my example.

I could redefine the empty pagestyle to act as plain, but I didn't want to do that. In fact, I tried that - and it works - but I also need empty pagestyles in my original document.
I suppose \part is like a book division, so it should look like another "cover" (what would explain why there's no number in the hm... back of the page). In my particular case, I need that number to be in there.
Does anybody have an idea?