For example, i run a bag forum where I allow members to buy and sell bag In the heading of each forum section I put each brand name, for example P R A X X and members are allowed to post their P R A X X bags there for sale. The second section I put C O A X X so for... I have already indicate very clearly on the front page of the website that Am I infringing their trademark? For example something like this
Having forum titles as you described is not going to be trademark infringement and I'll assume your domain name does not contain a trademark.
no the forum title has no infringement of trademark But if the forum allow members to buy and sell bags. If a few members post fake bags, will LV go after them or after the forum owner? For example, ebay has been sued by LV and other brands for selling fake bags http://edition.cnn.com/2008/BUSINESS/06/30/louis.vuitton/index.html
If your site is being used to sell knock-off bags, and you are aware of this, yes you can be held liable. You cannot create a marketplace for stolen or knock-off goods.
You can sue for anything, even using the name in a metatag - but as far as I know, there has never been a successful suit for a sub-folder - and I don't even think a sub-domain (there was one with google that was settled before it went to trial). http://caselaw.lp.findlaw.com/cgi-bin/getcase.pl?court=6th&navby=docket&no=03a0111p