At the beginning of your upkeep, if you have no cards in hand, each opponent loses 2 life.
At the beginning of each opponent's upkeep, if that player has no cards in hand, they lose 2 life.
The first ability checks whether you have no cards in hand both when it triggers and when it resolves. If you have any cards in your hand at the beginning of your upkeep, it won’t trigger at all. If you have any cards in your hand when the ability resolves, it does nothing.
The second ability behaves the same way, except that it’s checking your opponent instead of you.