Can I own an Air Gun that shoots BB's or Pellets?

Unless you have other convictions, the reason you may not possess a firearm is due to federal law, not California law (beyond the 10 year California prohibition). I'm not aware of any federal statue that prohibits a person convicted of a misdemeanor crime of domestic violence from possessing an air gun. Under California law, an air gun is not a firearm because there is no explosive propellant. My belief is that you may legally possess an air gun, however, there are restrictions as to where and how anyone can possess one, ie...schools, courts, and airports, etc... under California law.