Depending on where you enter (main door, store doors, etc.), you may or may not see a "no firearms" sign. It's been awhile since I've looked for any signage (I live in Tucson) but I'm pretty sure the mall owners take the position that firearms aren't allowed. Open carry inside and I'm sure you'll find out
Don't open carry (or carry discreet without a permit) in the food court - booze is served there so once you enter, you have passed the "it's only a trespassing violation" threshold and have entered the Class 3 Misdemeanor zone.