41 C.F.R. § 301-10.133

U.S. flag air carrier service is service provided on an air carrier holding a certificate under 49 U.S.C. 41102 (excluding a foreign air carrier operating under a permit), and which service is authorized by the carrier's certificate or by exemption or regulation. This also includes service provided under a code share agreement with a foreign air carrier in accordance with title 14, Code of Federal Regulations, when the ticket identifies the U.S. flag air carrier's designator code and flight number.