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This paper is concerned with two rather basic phenomena: the incoherent fluorescence spectrum of an atom driven by an intense laser field and the coupling of the atom to the (empty) modes of the radiation field. The sum of the many-photon processes gives rise to the inelastic part of the atomic fluorescence, which, for a two-level system, has a well-known characteristic three-peak structure that is known as the Mollow spectrum. From a theoretical point of view, the Mollow spectrum finds a natural interpretation in terms of transitions among laser-dressed states that are the energy eigenstates of a second-quantized two-level system strongly coupled to a driving laser field. As was recently shown, the quasi-energies of the laser-dressed states receive radiative corrections, which are nontrivially different from the results that one would expect from an investigation of the coupling of the bare states to the vacuum modes. In this article, we briefly review the basic elements required for an analysis of the dynamic radiative corrections, and we generalize the treatment of the radiative corrections to the incoherent part of the steady-state fluorescence to a three-level system consisting of 1S, 3P, and 2S states.