Augustine believes that Jesus is subject and addressee of the second Psalm. But why, in that case, does God tell him, “Ask of me, and I will give you the nations as your inheritance?” After all, Christ is God, too. Doesn’t he already have what the Father has? So why does he need to ask? Augustine explains as follows.

Postula a me, et dabo tibi gentes haereditatem tuam. Hoc iam temporaliter secundum susceptum hominem, qui sacrificium sese obtulit pro omnibus sacrificiis, qui etiam interpellat pro nobis; ut ad totam ipsam dispensationem temporalem, quae pro genere humano facta est, referatur quod dictum est: Postula a me; ut scilicet gentes nomini christiano copulentur, atque ita a morte redimantur, et possideantur a Deo. Dabo tibi gentes haereditatem tuam, quas possideas ad earum salutem, et quae tibi fructificent spiritalia.

Ask of me, and I will give you the nations as your inheritance. This now^[1] is said temporally according to the assumed man,^[2], who offered himself as a sacrifice to replace all sacrifices, who even intercedes for us, so that the statement, Ask of me, should be referred to that entire dispensation which was set up on behalf of the human race, that is, that the nations be joined to the Christian name, and thus be redeemed from death and possessed by God. I will give you the nations as your inheritance, so that you may possess them for their salvation, and so that they may bear spiritual fruits for you.

The translation is my own.