  The radiative self-energy correction to the bound-electron g factor of 2P_1/2
and 2P_3/2 states in one-electron ions is evaluated to order alpha (Z alpha)^2.
The contribution of high-energy virtual photons is treated by means of an
effective Dirac equation, and the result is verified by an approach based on
long-wavelength quantum electrodynamics. The contribution of low-energy virtual
photons is calculated both in the velocity and in the length gauge and gauge
invariance is verified explicitly. The results compare favorably to recently
available numerical data for hydrogenlike systems with low nuclear charge
numbers.
