I'm specifically interested in critical responses at the time to the publications of Howard's "Conan" stories and to Burroughs' "Barsoom" novels. Were they well received or were they panned by critics?
Bonus question: Were either of them considered to be financial successes?
A New York Times article calls Edgar Rice Burroughs "the most widely read American author of the first half of the twentieth century " and estimates his book sales at 60 million. Tarzan in particular was a popular icon and also produced a merchandising and media empire: comics, movies, toys, and all the rest. In 1919, Burroughs bought a huge 540 acre estate in the San Fernando Valley with a mansion overlooking Ventura Boulevard that belonged to the publisher of the Los Angeles Times. The price was $125,000, the equivalent of $1.8 million today.
While we have critical response and analysis of stuff like Twilight and Harry Potter and Star Wars today, writers like Howard and Burroughs were simply nonexistent as far as critics were concerned. Burroughs himself agreed (NYT again):
One reason for Burroughs's undeserved ostracism is the stigma attached to pulp fiction. According to the laws of the cultural jungle, writers like Hemingway or Fitzgerald are literary lions; Burroughs and other paid-by-the-word authors of science fiction, westerns, whodunits, and romantic confessionals are monkeys with typewriters--hacks. Burroughs pretended not to mind his lowbrow status. "I don't think my work is `literature,' I'm not fooling myself about that," he told the Los Angeles Times. Writers of his ilk, he volunteered with a shrug, belong "in the same class with the aerial artist, the tap dancer, and the clown."