Estimates for solutions to the transport equation under the perturbation of its attenuation and scattering terms

The aim of the paper is to give $L^p$-estimates for the weak solution to the transport equation with $L^\infty$-perturbation both of the attenuation coefficient and of the scattering kernel. We try to clarify the constants in our estimates, and we show the estimates by a direct calculation. We introduce the albedo operator for the solutions, and we show stability of perturbed albedo operators.