If you are talking about The Book of One Thousand and One Nights
(which is often referred to as Arabian Nights), then it contains
various authors.
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The One Thousand and One Arabian Nights was not written by a
single person. It is a compilation of very interesting stories
written by many and handed down orally through generations.
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If you are talking about the play The Arabian Nights, then it
was written by Mary Zimmerman.