From my friends at hollywoodmemoir.com
Hugh Martin (August 11, 1914 – March 11, 2011) was an American musical theatre and film composer, arranger, vocal coach, and playwright. He is best known for his score for the classic 1944 MGM musical Meet Me In St. Louis, in which Judy Garland sang three Martin songs, "The Boy Next Door", The Trolley Song, and Have Yourself a Merry Little Christmas. The last of these has become a Christmas season standard in the United States and around the English-speaking world and is widely considered one of the greatest Christmas songs of all-time. Martin became a close friend of Garland and was her accompanist at many of her concert performances in the 1950s including her legendary stint at the Palace Theater.
http://www.hollywoodmemoir.com/hugh-martin