My actionbar does not use an icon or a title, this makes the click area of the "up" button very small. How can I have a larger click area without a title and icon in the actionbar?
You can put an image where the app icon would be. Just make a transparent image to the width and height for each drawable size you need and put it in the drawable folder, call the image logo (@drawable/logo). You then need to tell the activity to use the logo, it's not hard and these links should help.
http://developer.android.com/guide/topics/ui/actionbar.html
http://developer.android.com/guide/topics/manifest/application-element.html#logo