Like most things in welding, depends. What do you want to do with this joint? It seems like an odd combination, 440 A, B, or C in the hardened condition is a martenistic stainless used primarily for its wear resistant properties and moderate corrosion resistance, whereas 304 (18-8) is an austenetic stainless used chiefly for its corrosion resistance. The yield for 440C fully hardened is around 200K yield, while 304 would normally come in around 30K. Welding should be possible, but not easy, the 440 has a carbon content of ~ 1.0%, making a high preheat mandatory. Further, welding would very probably interfere with the hardened condition of the 440 in the area of the weld. Brazing might be a better way of joining. With proper filler selection, a braze should be able to develop 40-45K ultimate tensile, which would be close to the UTS of the 304.