After some experimentation, here is what I have found out. Perhaps others may find it useful.
If you define array, list, or collection as the return value, it does not work:
    @GET 
    @Produces("application/json") 
      public String[] getIt() {   // THIS DOES NOT WORK
        ...
      }
However, if you wrap your collection in another class, it works:
   @XmlRootElement
   public class MyItem {
       public String[] items;
   }
    @GET 
    @Produces("application/json") 
      public MyItem getIt() {   // THIS WORKS
        ...
      }
This seems to be a limitation in Jersey's implementation. A similar web service under Windows (WCF) does not have an issue returning String[] from a web service method.
Regards,
Peter