According to Meyer's NT Commentary, many commentators have taken different positions on this question, those that view 15-21 as a continuation include Chrysostom, Theodoret, Jerome, Estius, Bengel, Rosenmüller, Tittmann, Knapp, Flatt, Winer, Rückert, Schott, Baumgarten-Crusius, de Wette and Möller, Hilgenfeld, Ewald and Holsten. Those opposed include Theodore of Mopsuestia, Oecumenius, Calvin, Beza, Grotius, Semler, Koppe, Matthies, Hermann, Hofmann, Wieseler and Reithmayr.
I take the former view, for the following reasons:
It seems unlikely that Paul would stand up and oppose Peter publicly with a dozen words. In a time and culture that highly valued oration1. A short speech including explanation, justification and exhortation is much more likely
14But when I saw that their conduct was not in step with the truth of the gospel, I said to Cephas before them all, “If you, though a Jew, live like a Gentile and not like a Jew, how can you force the Gentiles to live like Jews?” ESV
The 'we' in verse 15 can refer to Paul and Peter, but can't refer to Paul and the Galatians, who appear to be mostly gentile2
15We ourselves are Jews by birth and not Gentile sinners; ESV
Paul's conclusion in verse 21 exactly sums up the essence of his rebuke to Peter, who was tacitly condoning the opponents of the Gospel who were preaching by their actions that righteousness comes through the law
21I do not nullify the grace of God, for if righteousness were through the law, then Christ died for no purpose. ESV
Paul does explicitly address the Galatians again in the next verse
3:1O foolish Galatians! Who has bewitched you? It was before your eyes that Jesus Christ was publicly portrayed as crucified. ESV
1 c.f. Paul's speech in Acts 17 for example
2 See for example 1:13-14 where Paul speaks of 'Judaism' as '...the traditions of my fathers'