I want to make a minature version of the site I am working on available to wap users... Can I host this on the same webspace of the original HTML site or do I need specialised hosting?

you should be able to put anything on your hosting... its just a matter of being able to read it

wap is not a server-side language, it's based on xml. there's no need for a special host...

I'm actually wondering what one would need to make his website availiable for wap users. Would plain HTML work already and are there any restrictions? I'm asking, because my website is running smoothly on every browser, but getting it to work with wap would be really cool.