WEIGHTED SOBOLEV SPACES FOR LAPLACE-EQUATION IN R(N)

This paper establishes a wide range of isomorphisms for the Laplace operator in weighted Sobolev spaces, similar to the spaces W-m,W-p (R(n)), but with weights that prescribe the growth or decay of functions at infinity. These weights, which arise naturally from Hardy's inequalities, permit to prove fundamental weighted Poincare inequalities relating the norms of functions to that of their derivatives. This approach allows a fairly easy derivation of several results previously established by other authors and it completes them by new results.