In Ephesians 2:2, Paul describes the state of the unredeemed: 'Wherein in time past ye walked according to the course of this world, according to the prince of the power of the air, the spirit that now worketh in the children of disobedience.' The phrase 'the prince of the power of the air' — ton archonta tēs exousias tou aēros — names the operational sphere of the fallen power. The 'air' here is not the literal atmosphere but the spiritual atmosphere of the world below the heavens — the realm of human disobedience that the fallen one has, by permission and within limits, made his working ground.
John's Gospel uses a parallel title: 'the prince of this world.' Christ uses it three times — in John 12:31, 14:30, and 16:11. Each use places the prince in the same posture: he is about to be cast out, he has no claim on Christ, and his judgment is already announced. The fall of the prince of this world is, for John, simultaneous with Christ's lifting up on the Cross.
Paul, in 2 Corinthians 4:4, uses yet another variant: 'the god of this world' — ho theos tou aiōnos toutou — who has blinded the minds of unbelievers. The titles are coordinated. The fallen one operates as ruler, as prince, as god — but always in a sphere that is temporary, bounded, and under sentence. Ephesians does not call him the prince of heaven but the prince of the air. The heavens belong to Christ; the lower atmosphere of disobedience is the only ground the fallen one has left.
Patristic and Reformation theology read all three titles as descriptions of the same enemy in his current operational mode. The Adversary's claim to rulership is real for those who give him their disobedience, but it is illegitimate, temporary, and on the way to revocation. The ascension of Christ is, among other things, the announcement that the air over the world now has a new King.
Christ ascended into the very air the fallen prince claimed, leading captivity captive (Ephesians 4:8) — the territory of disobedience has a new King.