How to develop web live streaming in iOS

I want to build a website that can run on Safari. I need it to work on iPhone at least and ideally also on iPad. The basic idea is to give gamers the ability to live stream their game play live and enable them to also talk during the play so people can see and hear them live on YouTube. So technically what I need is to develop something that can capture the screen (video) and microphone (audio). And then I need to somehow send what I capture to YouTube live streaming. Since it is going to be a website, the language I intend to use is JavaScript.

Do you know any good libraries I can use in order to achieve that?

Thanks Danny