? a review of the book and one of the movie My own judgment is that the substitution sounds odd so I would be inclined to call the PP a complement. If it is, then the extraction behavior of the sentences in (1) is more or less expected. Otherwise, not.
B. The following sentences are under discussion:
(1) a. Which book did you see a review of in the Times?
b. Which book did you expect to see a review of in the Times?
c. Which book did a review of appear in the Times?
d. Which book did you expect a review of to appear in the Times?
Here are the structures for these sentences:
C. The standard judgments in the literature about the sentences in (1) are that (a) and (b) are grammatical while (c) is not. Judgments vary on (d).
D. Under the treatments of subjacency and the ECP given in the text, the grammaticality of (a) and (b) are expected. Because the DP "a review of X" has no specifier, it is not a barrier. The embedded infinitival IP in (b) is also not a barrier because it is governed by a verb. By the definitions of lexical and antecedent government the trace in both sentences meets the requirements for both types of proper government.
Sentence (c) should also be grammatical by the account in the text but it seems not to be. This problem might be remedied if we said that, like an infinitival IP, a non-branching DP has to be lexically governed in order not to count as a barrier. Under that stipulation (c) would violate subjacency and the ECP.
Given the proposal in the preceding paragraph and the stipulation that infinitival IPs governed by a verb are not barriers, (d) should be grammatical.