A lighting unit according to the invention comprises an electrodeless low-pressure discharge lamp and a high-frequency supply. The electrodeless low-pressure discharge lamp is provided with a discharge vessel which is closed in a gastight manner, comprises an ionizable filling, and has an enveloping portion and a recessed portion surrounded by the enveloping portion, which enveloping and recessed portions of the discharge vessel each support a luminescent layer. The electrodeless low-pressure discharge lamp is in addition provided with a coil which is arranged in the recessed portion of the discharge vessel and which is electrically connected to the supply. The conversion efficiency of the luminescent layer on the recessed portion is relatively high compared with that of the luminescent layer on the enveloping portion. This measure renders possible a lower temperature of the core.