A fuel injector in a combustor apparatus of a gas turbine engine. An outer wall of the injector defines an interior volume in which an intermediate wall is disposed. A first gap is formed between the outer wall and the intermediate wall. The intermediate wall defines an internal volume in which an inner wall is disposed. A second gap is formed between the intermediate wall and the inner wall. The second gap receives cooling fluid that cools the injector. The cooling fluid provides convective cooling to the intermediate wall as it flows within the second gap. The cooling fluid also flows through apertures in the intermediate wall into the first gap where it provides impingement cooling to the outer wall and provides convective cooling to the outer wall. The inner wall defines a passageway that delivers fuel into a liner downstream from a main combustion zone.