How did paul persuade the Corinthians to accept his authority?

Saul (as his name still was at that time) began to preach with fervor in the synagogues of Damascus that Jesus is the Son of God. Acts 9:22 (NIV) says that he "grew more and more powerful and baffled the Jews living in Damascus by proving that Jesus is the Christ." He had been a prominent Jewish figure (a Pharisee on his way to greatness and power in the Jewish world) before his conversion, so he knew all of the Old Testament prophesies and was able to effectively communicate Jesus' fulfillment of them. Through his preaching, and the testimony of Barnabas (a trusted brother who was convinced of Saul's conversion), the Corinthians came to accept Saul's authority as a Christian.