It has been suggested that the speeches attributed to Peter in Acts of the Apostles provide us with access to a summary of Petrine preaching, or at least an example of the early Christian preaching of the Jerusalem Church. C.H. Dodd wrote that, "In short, there is good reason to suppose that the speeches attributed to Peter in the Acts are based upon material which proceeded from the Aramaic-speaking Church at Jerusalem, and was substantially earlier than the period at which the book was written." (p.25)
The Case for a Pre-Lucan Source
Within the tradition of history, Luke would have had ample allowance to have been relatively creative in his speeches. However, to appeal to this in order to dismiss the speeches in Acts does not take note of Luke's own tendencies where he can be checked. For example, his use of Mark (and comparative use of Q) demonstrates considerable care in use of his sources when attributing sayings to Jesus. Similarly, we are able to compare the speeches attributed to Paul with his own epistles. Dodd writes that Paul's speech to the Ephesian church in Acts 20:18-35 "contains so many echoes of the language of Pauline epistles that we must suppose, either that the writer had access to these epistles (which is on other grounds improbable), or that he worked upon actual reminiscence of Paul’s speech upon this or some similar occasion." Dodd goes on to suggest that (in light of the "we" passages) that although we are not receiving a verbatim report, they may be "based upon a reminiscence of what the apostle actually said."
Regarding the Petrine speeches, Dodd points towards the existence of Semitisms, more specifically Aramaisms that are reminiscent of the sayings of Jesus in the Gospel tradition. Evidently, he concludes that somewhere along the chain - whether written, oral or received in translation - the ultimate source was Aramaic. While the presence of these Semitisms has found support, others have disagreed seeing them as resulting from Semitisms within the Septuagint. Of course, this isn't to deny the presence of Lucan stylistic and theological imprint, however, there is insufficient reason to see this necessitate that Luke was merely presenting his own Gospel. Furthermore, Stanton has convincingly argued that Luke was redacting a source in studying the use of Old Testament allusions and citations and presence of primitive Christian exegetical traditions.(p.71ff.) Noting the manner in which these were redacted, Stanton concludes that it "discounts the possibility that Luke is merely summarising his own Gospel or freely composing these verses." (77)
Part 2: This will present the common themes in the speeches of Peter as representative of some sort of Kerygma. Peter's? Jerusalem Church? Some Aramaic Christians?
Part 3: What's missing? How does it compare to a Pauline Kerygma? Something along those lines.
C.H. Dodd, Apostolic Preaching and Its Developments: Three Lectures With an Appendix on Eschatology and History.
James D.G. Dunn, Unity and Diversity in the New Testament: An Inquiry into the Character of Earliest Christianity
E.E. Lemcio, “The Unifying Kerygma of the New Testament”, Journal for the Study of the New Testament 1988, pp. 3-19, and 1990, pp. 3-11
Graham N. Stanton, Jesus of Nazareth in New Testament Preaching (Society for New Testament Studies Monograph Series)