Basil Leaves, Black Spots

About two weeks ago I planted two Genovese basil plants I had purchased from you. They were planted in a very large container in new, good-quality potting soil. Today I noticed that although the upper leaves are growing nicely and have good color, the lower leaves have black spots and are falling off.
Can you tell me what the cause of this problem might be, and how to treat it?

Since the conditions in your growing area are probably different from those in ours, the tender basil leaves grown by us might not be able to survive in your conditions. Since the plants have good fresh soil, they are growing new leaves that are perfectly suited to their growing conditions and are allowing the old leaves to senesce. Dying leaves are a perfect host for every opportunistic fungus spore carried onto them by the aircurrents. The black spots are the sites of infection and those leaves should be picked off by you and destroyed. That way they cannot produce new spores that just wait for the plant to be stressed in any way and then attack other leaves.
Also make sure that plants are dry by nightfall since damp leaves allow spores to stick to them and grow into their tissues during the night. Good air movement is another preventative measure, because it does not allow any spores to settle down onto leaves, but keeps them suspended in air.