iTunes says I do not own the application

If the App Store application on your Apple touch device (iPhone, iPod touch, or iPad) says that you cannot download the update because you do not already own the application, make sure that the iTunes Store account that was used to purchase the application is the currently active iTunes Store account on your device. This can be reviewed and changed in the device’s Settings application under Store.

If you still have trouble, please try downloading the update within iTunes on your computer and then sync the updated application to your device using the USB cable.