Well, we know that Barsoom was an influence in the early design phases of Dark Sun because the designers of the setting have said so - they've been very clear about this fact on a number of occasions. In its initial concept, DS was much closer to Barsoom, but TSR's marketing folks asked for a number of changes. Initially, all or most of the races were exotic and the PHB races did not feature (no dwarves, no elves, no halflings etc). The marketing guys decided that this would prevent customers from buying into the setting, so they asked for those races to be included. The designers agreed, but made them into the warped Athasian versions that feature in the published setting.