This talk will describe results about the L^p properties of functions that are solutions of Laplace's equation in Rⁿ - especially R³. The interest is in describing these properties for electrostatic or gravitational fields. For these fields the important constraint is that the fields have finite energy - or that their gradient be in L² and that the scalar potential of the field vanish at infinity. The Sobolev imbedding theorem in this case says that the potentials of finite energy fields on R³ are precisely in L⁶(R³). I shall show that when L^q assumptions on the Laplacian of the function are added then there are a range of new imbedding results. In particular the fields will be continuous and bounded under some natural assumptions. Moreover the Hilbert space case involves a Reproducing Kernel Hilbert space with potential functions that need not be in L²(R³).