Just taking the definition of freedom of speech at its most basic, face value level, the answer is yes. Just like if I cuss out my boss he can fire me. You don't have freedom of speech at work. You don't have it in school to a certain extent. You don't have it at home if you're a kid. There are many places where you don't have freedom of speech. I can't demand that the local top rated station hire me so I can talk on the air.OK, Let's say you are on the air doing a talk show. Someone calls in to promote the local Ku Klux Klan. You slam the phone and cut him off.
Does that mean you infringed on his freedom of speech?
But that doesn't mean that your First Amendment rights are being violated. First Amendment rights come into play if an arm of the government is regulating or banning speech, usually public speech. Any arm of the government decides to ban someone's speech, they'd better have a really good and solid reason that will pass muster with the Supreme Court of the United States, because the Supreme Court does not take the First Amendment lightly.