This is a tricky area of immigration law, so you REALLY need to do your own research, possibly pay a lawyer, and be sure that you have the right answer (rather than just trusting the advice of strangers on an internet forum), before embarking on such a venture.
Having said that, I can tell you that I spent a good bit of time researching the options for working abroad a few years ago. My guess is that you would not need a U.S. "work visa." That is for someone who comes to the U.S. and gets a job working for a U.S. company as an employee. You would, however, most likely need a business license, and I am sure that some sort of permit to operate a business as a foreign citizen would be required.
You would not be an employee of any U.S. company, but you WOULD be operating your business in U.S. territory. I do not know the details, but I would bet a HUGE amount of money that the U.S. has restrictions (paperwork, fees, etc.) on foreign citizens who want to operate a business in the U.S.
Indeed, all countries that I am aware of have some such restrictions.