The thing to consider, as Philip says, it not to bury or suffocate the roots of the Japanese Maple. You need to assume it has roots outwards from the trunk at least as far as the branches reach, and possibly further. So I'd say your raised beds would be fine, but keep them at least maybe 10ft. away from the trunk of the tree.
The flip side you might find eventually is the tree putting roots up into your raised beds because of all the fert and water you'll be giving your vegetables. I have an 18in. high, 3ft. X 12ft. raised bed in the middle of my back yard, at least 30ft. from the nearest (large and lusty) oak tree but that bed is now chock full of oak tree roots. I'm going to have to pay a lusty young person to dig it all out and sift the soil for me before I can really grow much in there now.
