Areas of Low Rainfall Over the Sea?

Are there “deserts” over the open ocean (which is to say, are there patches of the ocean, like there are over land, where rainfall is very low)?

Certainly. Rain is caused by clouds after all. In areas where there aren’t many clouds there isn’t much rain. For a detailed look at rain over the entire globe, visit TRMM:
http://trmm.gsfc.nasa.gov/

The Sargasso sea has been described as an ocen desert.