Question: Who wrote "All I Want For Christmas Is You" with Carey?
About the article "All I Want for Christmas Is You", section "Abstract".

Candidate passages:
"All I Want for Christmas Is You" is a 1994 song by Mariah Carey.
All I Want for Christmas Is You may also refer to:  "All I Want for Christmas Is You" (Vince Vance & The Valiants song), a 1989 song by Vince Vance & The Valiants (lead vocal: Lisa Layne)  "All I Want for Christmas Is You", a 1966 song by Carla Thomas  "A Christmas Love Song" (music: Johnny Mandel and lyrics Alan Bergman and Marilyn Bergman) The first line of the lyric reads "All I Want for Christmas Is You", and recordings may be mislabeled with this as the "title".  
"My Only Wish" received mixed reviews from music critics.
It has been compared to "All I Want for Christmas is You" by Mariah Carey.
Grace Cicciotti of iphone.funweek, commented, the two items in question, in fact, closely resemble, perhaps too much.
"My only wish", written by "The-Dream" has the same melody of "All I Want for Christmas is You ', the same high note and even the same meaning: not change much between all the phrase 'All I want for Christmas is you baby "and" My only wish for Christmas is you'.
In summary, it appears that much of Jessica suffers a lack of inspiration ... MTV said, we know that Mariah Carey has returned to the yuletide jam with her Merry Christmas II You.
And now we get some Christmas spirit from Jessica Simpson, with the jaunty, playful "My Only Wish."
Not unlike Mariah Carey's "All I Want for Christmas Is You", Simpson's track covers up some heartache with a buoyant and peppy track, complete with Salvation Army Christmas bells and fireside pianos.
GAWKER commented, "Is Jessica Simpson's New Christmas Song a Complete Mariah Carey Rip Off?".
Jessica Simpson debuted the first single from her upcoming Christmas album, called, "My Only Wish (For Christmas Is You)."
One problem: it's a total rip off of Mariah Carey's "All I Want For Christmas Is You."
Carey performed the song for the first time in a pre-recorded performance on November 19, 2010, at NBC's Rockefeller Center Christmas Tree Lighting, which aired on November 30, 2011.
On December 3, 2010, Carey performed "Oh Santa!"
as well as "All I Want For Christmas Is You" at the Walt Disney World Christmas Day Parade special, which featured Carey surrounded by dancers, including ballerinas and cheerleaders, and ended with fireworks at the end of the performance.
Carey then performed the song as part of a set list on her own one-off Christmas television special, entitled "Mariah Carey: Merry Christmas to You."
In addition to performing "Oh Santa!
", Carey also performed her cover of "Charlie Brown Christmas" and a medley of "O Come All Ye Faithful/Hallelujah Chorus," featuring her mother, Patricia Carey, as well as various other songs from both of her Christmas albums. 
Merry Christmas II You is the second Christmas album by American singer-songwriter Mariah Carey.
The album was released on December 23, 2010, just before Christmas and features four original songs, covers and medleys of several traditional Christmas songs, and a re-recorded version of her 1994 Christmas hit "All I Want for Christmas Is You".
It was re-released on 14 January 2011 as Merry Christmas 2 U. 
"Oh Santa!"
was one of four new songs which Carey co-wrote and co-produced alongside longtime collaborators Jermaine Dupri and Bryan-Michael Cox, for her second Christmas album, "Merry Christmas II You" (2010).
The song premiered on AOL on October 1, 2010 and was released via digital download by iTunes on October 11, 2010.
According to sheet music published at Musicnotes, "Oh Santa!"
is an upbeat pop song which incorporates the musical genres of Christmas, R&B and Dance-pop.
The song is written in common time with a moderate tempo of 80 beats per minute and is written in the key of C major, with Carey's vocal range spanning from the low note of B2 to the high note of F6.
Carey also recorded a mix of "Oh Santa!"
and her signature christmas song "All I Want for Christmas Is You", entitled "Oh Santa!
All I Want for Christmas is You (Jump Smokers Holiday Mashup)", which was made available to download via iTunes on December 17, 2010.