Poking around the REST API, I don't see a way to get the space owner. I can get the permissions list, but it is confusing, since there are many entries (duplicates!) that don't mention an operation at all.
I'm using this Python wrapper: https://pypi.python.org/pypi/PythonConfluenceAPI. I'm not sure if that's limiting my options, but the raw REST API docs don't provide any clues.
Can you please clarify what do you mean by Space Owner? Technically, in Confluence you do have a space permissions and it doesn't have owner. However, people with Space Administrator permissions can consider as an owner in most of the use cases. I would recommend you to take look at space permissions document as well :-)