The fast component of the barium fluoride (BaF2) crystal luminescence with the emission peak at 220 nm allows those crystals to be employed in fast calorimeters operating in harsh radiation environment. However, the slow component with the emission peak at 330 nm and about 85% of the total emission light could create big problems when working at a high radiation rate. In this work we report results of tests of multilayer filters that can suppress luminescence in the range from 250 nm to 400 nm, which covers most of the BaF2 slow component luminescence. The filters are made by spraying layers of rare earth oxides on a quartz glass substrate. Filters typically comprise 200-220 layers. A few filters were prepared by spraying thin layers on quartz glass. The filters have a peak transmittance of about 70-80% in the range of 200-250 nm. Measurements of the light output of the BaF2 crystal with and without a filter between the crystal readout end and the PMT demonstrate substancial suppression of the slow component. To our knowledge, this kind of filters are produced and tested for the first time.