Jamieson, Fausset and Brown on Acts 2:29-36

29-36. David ... is ... dead and buried, &c.--Peter, full of the Holy Ghost, sees in this sixteenth Psalm, one Holy Man, whose life of high devotedness and lofty spirituality is crowned with the assurance, that though He taste of death, He shall rise again without seeing corruption, and be admitted to the bliss of God's immediate presence. Now as this was palpably untrue of David, it could be meant only of One other, even of Him whom David was taught to expect as the final Occupant of the throne of Israel. (Those, therefore, and they are many, who take David himself to be the subject of this Psalm, and the words quoted to refer to Christ only in a more eminent sense, nullify the whole argument of the apostle). The Psalm is then affirmed to have had its only proper fulfilment in Jesus, of whose resurrection and ascension they were witnesses, while the glorious effusion of the Spirit by the hand of the ascended One, setting an infallible seal upon all, was even then witnessed by the thousands who stood listening to Him. A further illustration of Messiah's ascension and session at God's right hand is drawn from Psa 110:1, in which David cannot be thought to speak of himself, seeing he is still in his grave.