There has to be a reason as to why its the worst soil. Look at the trees and find out a bit more about them. Some trees like people don't like competition, so they take preventive measures. Some for example like these
http://en.wikipedia.org/wiki/E... exude a sap/resin which prevents any thing from growing under them. A way to check it is to park your car under them. Check the windscreen against strong light, if you see droplets then scowl at the trees. Use a mirror if a car standing there all day is not feasible.
Regards,
Arif.