Has a very easy answer in the US: No. You do not own your airspace. The FAA owns your airspace. You can build a tall structure (subject to local laws). But anything above that is outside your control. --- This article, however, is about Ireland.
That's not true for helicopters and UAVs within sight of their controllers, but I feel sorry for the people who bought a house not near and airport, and now have to deal with a buzzing swarm overhead.