Jerod's Jewelry in Crestview Hills

First, i'm always OC where legal. I stopped at Servati's in Crestview Hills over the weekend. I was getting back in the car and noticed that Jared's had a sign on their window regarding the carry of deadly weapons, etc. I guess the part that surprised me was "onto this land, parking lot, or premises." it's a shared parking lot with several other businesses.
What do you guys think about the legality of this?

1)There is no legality or legal backing regarding this sign.

2)I think they can display whatever sign they want to--the problem comes if they try to enforce it. Perhaps that's where your question lies. I think everyone would agree that they may ask you to leave their store. Do they have the authority to ask you to leave the parking lot? Probably not because they probably don't own it. I suppose the landlord could ask you to leave.

Servati's is a Cincinnati based company, so they send out Cincinnati signs, just like 5/3rd Bank, that I ignore.

It's always fun to bring it to their "misinformed" attention that they have no legal rights to stand upon with their signage. That look in their eyes is more priceless than one of their over-priced diamonds. *LOL*