Airpower Missions in the Maritime Domain

In the course of writing an article about the organizational politics of airpower, I'm defining the most common missions expected of air units. These include close air support, reconnaissance, air mobility, interdiction, air superiority, decapitation, and the various types of strategic bombing. In the context of this typology I've run into a problem describing airpower missions in the maritime domain; should commerce protection (primarily anti-submarine warfare) and anti-surface air operations be considered independent missions, or do they fall into the more general airpower missions described above (including any general missions that I may have missed)?

I would appreciate any thoughts on the question from commenters, as well as pointers to publications that deal with these definitional questions.