This is that - This is the fulfillment of that, or this was predicted. This was the second part of Peter's argument, to show that this was in accordance with the predictions in their own Scriptures.
By the prophet Joel - Joel 2:28-32. This is not quoted literally, either from the Hebrew or the Septuagint. The substance, however, is preserved.

Spoken by the prophet Joel - The prophecy which he delivered so long ago is just now fulfilled; and this is another proof that Jesus whom ye have crucified is the Messiah.

But this is that which was spoken by the (k) prophet Joel;
(k) There is nothing that can dissolve questions and doubt except testimony taken out of the Prophets: for men's reasonings may be overturned, but God's voice cannot be overturned.

But this is that which was spoken by the prophet Joel. This affair, which is a matter of wonder and amazement with some, and of speculation with others, and of ridicule and contempt with the most, not the effect of wine, but the fulfilment of a prophecy in Joel 2:28 and is that effusion of the Spirit there foretold; and this prophecy is by the Jews themselves allowed to belong to the world to come, or to the times of the Messiah. Some of their commentators (o) say, that it refers "to time to come"; by which they frequently mean the times of the Messiah; and another says (p) expressly, that they belong , "to the days of the Messiah"; and in one of their Midrashes (q) it is observed, that "the holy blessed God says in this world they prophesy single, (particular persons,) but "in the world to come" all "Israel" shall become prophets, as it is said, Joel 2:28 "and it shall come to pass afterward, that I will pour out my Spirit upon all flesh, and your sons and your daughters shall prophesy, and your old men", &c. So expounds R. Tanchums with R. Aba.
(o) Jarchi in Joel ii. 28. & R. Jeshuah in Aben Ezra in loc. (p) R. David Kimchi in loc. (q) Bemidbar Rabba, sect. 15. fol. 219. 2.

This is that which was spoken. He turns to their prophets for an explanation.
By the prophet Joel. Who lived about 800 B. C. See Joel 3:1-5.

But this is that which was spoken of by the prophet - But there is another and better way of accounting for this. Joel 2:28