Exegesis:

en Beelzeboul tō archonti tōn daimoniōn ekballei ta daimonia lit. ‘in (the power of) Beelzebul, the ruler of the demons, he drives out the demons.’ en Beelzeboul is best understood as ‘through,’ or, ‘with the help of Beelzebul.’

archōn ‘ruler,’ here the ruler of an hierarchy of evil spirits, or, demons.

Translation:

By Beelzebul should be given emphasis, cf. “it is through B., …, that he casts demons out” (The Four Gospels – a New Translation), or changing the sentence structure, ‘because B., …, gives him power (or, enables/helps him), he can cast out demons,’ ‘B. he uses/takes to chase out demons’ (Sranan Tongo).

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.