The Songwriters Hall of Fame lists:

BLUE FEDORA
Writer: Bud Green and Albert Van Dam
Publisher: Anne-Rachel Music Corp./EMI Robbins Catalog, Inc.

It also says (here):

[Bud Green] was commissioned by Hollywood during the 30's and 40's and Green songs can be heard in the Hollywood musicals Syncopation, Mother's Boy, Lucky in Love, Big Boy, Show in Hollywood and Baby Take a Bow.

Some other songs by Bud Green, posted at Mudcat:
ALABAMY BOUND
AWAY DOWN SOUTH IN HEAVEN
FLAT FOOT FLOOGIE
SENTIMENTAL JOURNEY
THAT'S MY WEAKNESS NOW
THE MAN WHO COMES AROUND