Well, since its a Friday and you took the first step . . .
Wow, an opinion by Justice Stewart. This really reaches back. Good find but its slightly off topic. Although the speech in Hudgens occurred at a mall, the Supremes brushed off the shopping mall issue and focused on this as a dispute involving union organizers governed by the National Labor Relations Act rather than as a hard core free speech case (see, e.g., nude dancing cases, below). Hudgens decided what kind of union solicitations are permitted on the property of an employer, and under what circumstances. Tracking the progeny of Hudgens indicates that it is cited as controlling in labor disputes not free speech cases, with the following exceptions:
The only subsequent Supreme Court case dealing with Hudgens in any depth that comes close to the shopping mall issue was Carey, States Attorney of Cook County v. Brown (1980). In that case the Supremes invalidated a local anti-picking law, holding that peaceful protesters could run a picket line in front of the Mayors house (he must have loved that). But the issue was an Illinois law that allowed peaceful picketing by unions, but not by anyone else, violating the Fourteenth Amendment.
Shopping Mall Law: I think the load star case at the Supreme Court involves not a shopping mall but another type of heavily utilized non-public foruman airport. In Intl. Soc. for Krishna Consciousness. v. Port Authority, Justice OConnor wrote in 1991 that publicly owned airports are not public fora. Unlike public streets and parks, both of which our First Amendment jurisprudence has identified as traditional public fora, airports do not count among their purposes the free exchange of ideas. That meant that owner had the right to regulate otherwise protected First Amendment activities. That was the end of annoying leaflets in airports and the Krishnas, who lost their prime means of fundraising.
This same non-public fora argument has been used to uphold the right of private parade organizers to exclude those with viewpoints they dont (ahem) embrace, as in South Boston Allied War Veterans Council v. Irish-American Gay, Lesbian and Bisexual Group of Boston (1994), and to allow a university to charge an activity fee to fund general extracurricular political speech on campus (kind of the flip side: the private organization can require students to fund speech that some of them object to).
Searching with my rusty skills, I got over a hundred hits of appeallate cases. The ones that involved shopping malls either followed Justice Sandys non-public fora doctrine or were labor cases decided under Hudgens.
Now, if you dont mind, scholarship demands that I go back and examine those fascinating nude dancing cases involving free speech. . .