How to make a ramp affect other layers

I'm trying to create a lower thirds that will include some motion, otherwise I might try Photoshop for this. But basically, I'm trying to create a gradient using ramp in AE so that the lower thrids I've created fades away on the sides. Similar to the image I've attached. I don't know how to make the layer that I put the ramp effect on affect the other layers. Can anyone help?