Episode 3 of Free Speech Rules, starring UCLA law professor Eugene Volokh.
Can the law punish deliberate lies about public matters?
Well, it depends.
Here are the six rules of fake news:
False statements that tend to damage reputations can generally be punished.
Of course, the law doesn't call this "fake news"—it calls it "defamation."
Written defamation is called "libel." Spoken defamation is called "slander." Radio and TV broadcasts are usually considered libel, except in Georgia, where they're called "defamacast." No really, they made up a new word for it, and it's ... well ... it's not catching on.
Intentional lies about particular people or companies can lead to massive damages awards, including punitive damages. They can even lead to criminal punishment in states that still have "criminal libel laws," though such prosecutions are pretty rare.
Negligent mistakes about particular people or companies can also lead to damages awards, unless the statements are about public officials or so-called "public figures"—people or businesses who are quite famous or influential. Those plaintiffs have to show the speaker knew the statement was false or at least was likely false.
And in many states, some falsehoods about particular people can lead to damages even if they don't harm a person's reputation. That's called the "false light" tort. Classic example: Baseball great Warren Spahn once won a damages award because a biographer had falsely claimed that Spahn was a war hero—even though that tended to falsely enhance Spahn's reputation rather than harming it.