The principle or principles governing restrictions on speech such as limiting it on private property, or in situations like the aforementioned bullhorn outside your house, are collectively referred to as "Time, Place, and Manner" restrictions.
This is a reasonably good introduction to the topic:
http://www.answers.com/topic/time-place-and-manner-restrictions?cat=biz-finHere are several excerpts which cover the Berkeley situation (emphasis mine)
The First Amendment to the U.S. Constitution guarantees freedom of speech. This guarantee generally safeguards the right of individuals to express themselves without governmental restraint. Nevertheless, the Free Speech Clause of the First Amendment is not absolute. It has never been interpreted to guarantee all forms of speech without any restraint whatsoever. Instead, the U.S. Supreme Court has repeatedly ruled that state and federal governments may place reasonable restrictions on the time, place, and manner of individual expression. Time, place, and manner (TPM) restrictions accommodate public convenience and promote order by regulating traffic flow, preserving property interests, conserving the environment, and protecting the administration of justice.<snip>
Place restrictions regulate where individuals may express themselves. The Supreme Court has recognized three forums of public expression: traditional public forums, limited public forums, and nonpublic forums. Traditional public forums are those places historically reserved for the dissemination of information and the communication of ideas. Consisting of parks, sidewalks, and streets, traditional public forums are an especially important medium for the least powerful members of society who lack access to other channels of expression, such as radio and television. Under the First Amendment, the government may not close traditional public forums but may place reasonable restrictions on their use.<snip>
The government is allowed to regulate nonpublic forums with even greater latitude. Nonpublic forums include privately owned property and publicly owned property devoted almost exclusively to purposes other than individual expression. Airports, jailhouses, military bases, and private residential property have all been deemed to be nonpublic forums under the First Amendment. Public sidewalks and streets that abut private property normally retain their status as traditional public forums, however (Frisby v. Schultz, 487 U.S. 474, 108 S. Ct. 2495, 101 L. Ed. 2d 420 <1988>).
In nonpublic forums the government may impose speech restrictions that are reasonably related to the forum's function, including restrictions that discriminate against particular viewpoints. For example, in Perry Educ. Ass'n v. Perry Local Educators' Ass'n, 460 U.S. 37, 103 S. Ct. 948, 74 L. Ed. 2d 794 (1983), the Supreme Court ruled that a rival teachers' union could be denied access to public school mailboxes, even though the elected union representative had been given access by the educational association. This restriction was reasonable, the Court said, in light of the elected representative's responsibilities to negotiate labor agreements on behalf of the union.You can read the article if you would like a better understanding of what criteria such restrictions must meet in order to avoid violating the first amendment.