Within checking theory of the Minimalist Program, the checking domain of a head A consists of everything adjoined to it, and of its specifier(s). Formally, the checking domain of a head A is defined as the minimal residue of A. The residue of A is its domain minus its complement domain.
In the following structure (with a head H adjoined to X), the checking domain of X consists of UP, ZP, WP and H. The checking domain of H is UP, ZP and WP.
XP1 /\ / \ UP XP2 /\ / \ ZP1 X' /\ /\ / \ / \ WP ZP2 X1 YP /\ / \ H X2
Checking domain in Utrecht Lexicon of Linguistics
- Chomsky, Noam A. 1995. The Minimalist program. Cambridge, MA: MIT Press.