What is the best way to record and stream live video to many clients? Are there any libraries?
Check out Amazon EC2's streaming service, CloudFront. If you're trying to distribute content to a large number of clients, the elastic cloud trumps any other implementation cost-wise, and can easily be implemented in Java.
http://aws.amazon.com/cloudfront/
They have very helpful documentation for developers, and incredibly reasonable pricing for content delivery that easily beats the cost of setting up an in-house solution.