Some new and short proofs for a class of Caffarelli-Kohn-Nirenberg type inequalities

In this note we provide simple and short proofs for a class of inequalities of Caffarelli-Kohn-Nirenberg type with sharp constants. Our approach suggests some definitions of weighted Sobolev spaces and their embedding into weighted L-2 spaces. These may be useful in studying solvability of problems involving new singular PDEs. (C) 2007 Elsevier Inc. All rights reserved.