I'm not sure how qmail fits into this - are you not running it on the
same machine?

You might want to have a look at http://www.dnsstuff.com/ and see what
DNS records have been configured.

To do it programmatically from Java, see Robert's earlier reply.

If you mean that people in other parts of the world can do the reverse lookup
(using qmail -- whatever that is) but that the same people can't use Java to do
it, then I have no idea what could cause that.

If you mean that /you/ can do a reverse lookup (using qmail), but that /other
people/ can't do it (using anything), then that's not so very surprising.  In
this case qmail is running on the machine with the relevant IP address and is
not representative of any other machine on earth.

If you mean that you can use qmail (or something) on your local LAN, but
nothing works from elsewhere in the world, then that's just how DNS (and
networks in general) work.  Talk to your system administrators -- they will be
able to explain your set-up better than I can.

If you mean that some people (out on the Net) can use qmail (or anything) to do
a reverse lookup, but that other people in different parts of the world cannot,
then that indicates a screw-up in the DNS system somewhere and there is nothing
whatever you can do about it except talk to the people who are managing your
domain name.

   -- chris