Gun ownership is already restricted. That's the will of the people.
There are currently over 20,000 "gun control" laws on the books.
Anyone who has been convicted of a felony is banned by federal law from ever possessing “any firearm or ammunition."
Specifically, a person "convicted in any court of a crime punishable by imprisonment for a term exceeding one year" cannot possess any firearm in any location. 18 U.S.C. 922(g) is the federal law that prohibits anyone ever convicted of any felony to ever possess any firearm either inside or outside of his home.
The federal punishment for felon gun possession is up to 10 years in prison.
There are many other federal gun ownership restrictions.
For example, a conviction for a misdemeanor domestic battery results in a loss of gun rights.
A person who is the subject of an order of protection may not possess a weapon.