ActiveSync from Microsoft is designed to sync your personal information from the PC (running Outlook) to your Axim.
You can also use Exchange Server ActiveSync (EAS), which allows you to sync your personal e-mail, calendar and contacts over the Internet. (NB: This option requires a bit of work at the Exchange Server end: Getting OWA to work is typically the first step).
If you want to sync Public Folder information, you will need to investigate some other products: I have heard that
http://www.chapura.com/pmp_wm.php does this. How this syncs (through the PC or over the air/Internet), I don't know. And whether there is anything on the Exchange Server end, again: no ideas.