This is the question that I have posed to the students in my NT and Christian Origins class. It is a complex issue that I don't think has been adequately resolved yet. Some observations:
1. Acts 6:5 mentions Nicolaus a proselyte of Antioch. The Greek appears to me to be ambiguous: that Nicolaus was either a man from Antioch and a proselyte of the Jerusalem church, or already a proselyte from Antioch. If the latter, then there is an Antiochean church before Stephen's martyrdom. Since Nicolaus was also a "Hellenist" then this would support the Antiochean church as a Greek-speaking satellite of the Jerusalem church.
2. Acts 8:1 and 11:19 mention the dispersion of the Hellenists into Judaea, Samaria, Phoenicia, Cyprus, and Antioch. The mission work included, according to Luke, preaching to the Jews and the Gentiles (11:20).
3. Acts 9:29 says that the Hellenists are after Paul, seeking to kill him because of his preaching. How can this be reconciled with Acts 6?
4. Acts 11:22, 11:27-29, 13:1, 15:1, etc. There appears to be a strong network of missions established very early in the church with Jerusalem as the main center, while Antioch (and others) are satellites under the authority of Jerusalem. This is not the opinion of Luke alone since it is supported by what Paul tells us about his relationship with Jerusalem in his letters, a relationship that he struggles with.
5. What were the Antiochean Christians teaching? They had a Gentile mission. Were they circumcising? Were they following traditional Jewish diet? Did Jerusalem relax its attitude toward the Law as is implied by the story of the Jerusalem council and the letter that Luke says James sent to Antioch? What was going on in Antioch?