Who was Peter addressing in Acts chapter 3 shortly after Pentecost?
Peter was addressing the nation of Israel. Shortly after Pentecost, his language in Acts chapter 3 shows he was still speaking to Israel on covenant ground, pleading with them to recognize that the one they killed was their rightful king, whom God raised and would send back if they believed.
Les explains that Peter, still shortly after Pentecost, is addressing the nation of Israel, and the language itself shows this. Peter remains on covenant ground, tied to the Abrahamic covenant in which God called out one man to bring forth a nation, place them in a land, and eventually bring them their king, government, and kingdom so Israel could be the evangelization of the nations. Although Israel rejected this by crucifying their king, God had not given up on them or turned to the Gentiles. Peter is still pleading with Israel, saying the one they killed was the one they should have accepted as king, but God raised him from the dead and called him back to glory, and God is ready to send him back as their king if they believe.