The Yopy runs embedded Linux, its user interface relies on the kdrive tiny X-server and icewm. I have ported the GPL-version of Qtopia to the Yopy, which allows you to run a large number of existing Qtopia applications (for the Sharp Zaurus, for instance) on the Yopy. (My own motivation for wanting Qtopia was to be able to run my own personal applications using Qt on the Yopy, and I thought using Qtopia would be easier than using Qt for X. I have to admit that the amount of work necessary to port Qtopia was larger than expected, but on the other hand I'm very happy with the resulting system I have now.)
Qtopia runs on top of Qt/Embedded, a library that draws directly into the Linux frame buffer. Most devices running Qtopia therefore do not provide an X-server. My Yopy-port of Qtopia runs without stopping the X-server (but without any performance penalty--Qtopia draws directly into the framebuffer). Qtopia is started like any other application from the window manager. You can switch between Qtopia and X11 at any time. This allows Qtopia to rely on system services tied to the X-server (GMate's power and light demons use the X server as a messaging channel, and the CDMA phone jacket can only be used under X).
My Qtopia/Yopy port is used by a number of people in the Korean Yopy Users Group (KYUG), and you can find local copies of the Qtopia files, more information about this port as well as discussions on their (Korean) website. In particular, there is a Beginner's FAQ and a discussion on running Opera on the Yopy. You may find it easier to follow the Korean instructions for installing Yopy there if you can read Korean.
I did this port in the fall of 2003, and as far as I am concerned, this project is finished. I will not release any new versions of my Qtopia port (until Trolltech releases an interesting new version of Qtopia itself). The main reason is that I have modified my Yopy so much (in particular, I have Qtopia in ROM) that it is currently impossible for me to test releases on the standard Yopy device without reflashing my Yopy.