This article by Sanghwan Lee contends that the linguistic onment in Galilee was not exclusively and perhaps not predominately Aramaic, and that Greek was used far more widely than some scholars have contended. The basic contention of the article is as follows:

“First, the ipsissima verba of Jesus preserved in the Gospels strongly indicate that Jesus, a Gali- lean carpenter, was able to speak Greek.20 Secondly, since a conversation requires at least two parties (locutor and interlocutor), those who listened to the ipsissima verba of Jesus must have understood Greek. Thirdly, the members of the Galilean Q community who wrote down sayings of Jesus (in the 30s–40s) must have been able to write in Greek.”

The argument and evidence can be found here.