They did receive special recognition, but not in particularly positive ways; virtually all prophecy rages against them and denounces them for various kinds of wickedness. As the immediate southern neighbours of Judah, they encroached on territory that the Judahites considered theirs after the destruction of Jerusalem, and this is often cited as a primary reason for their antagonism. There's a good article on it if you can access it: Assis, E., "Why Edom? On the Hostility Towards Jacob's Brother in Prophetic Sources" in Vetus Testamentum, Vol. 56, Fasc. 1 (Jan., 2006), pp. 1-20.