Passing ball to self

[MiamiWadeCounty]

Supposing that A1 leaps in the air, catches the ball that was headed out-of-bounds, tosses it high enough so that after A1 lands out-of-bounds, he recovers and returns inbounds and then catches the ball, before it hits the floor. Is there a violation? In my thoughts, because A1 was airborne when he caught the ball, and threw it back over the playing surface, there would be no violation. However, if A1 had a foot or feet touching the playing surface and tossed the ball high enough so that after his momentum carried him out-of-bounds, he recovered, re-established himself inbounds, and then caught the ball before it hit the playing surface, we would consider his actions to be traveling, as expressed above.

Dribble
Art. 3. During a dribble, the ball may be batted into the air, provided that it
is permitted to strike the playing court one or more times before the ball is
touched again with either hand.

According to this rule, I pretty sure that's an illegal dribble violation in both situation.