who is the song writer?
Paul McCartney
Hey Jude
 It was written by Paul McCartney and credited to the Lennon–McCartney partnership. 
what song did paul mccartney wrote for julian lennon "Hey Jude" is it a song? Yes
wiki:1167007
Hey Jude [SEP] Introduction
"Hey Jude" is a song by the English rock band the Beatles that was released as a non-album single in August 1968. It was written by Paul McCartney and credited to the Lennon–McCartney partnership. The single was the Beatles' first release on their Apple record label and one of the "First Four" singles by Apple's roster of artists, marking the label's public launch. "Hey Jude" was a number-one hit in many countries around the world and became the year's top-selling single in the UK, the US, Australia and Canada. Its nine-week run at number one on the "Billboard" Hot 100 tied the all-time record in 1968 for the longest run at the top of the US charts.