The form boundedness criterion for the Laplacian operator

In this paper, we characterize the class of measurable functions (or, more generally, real- or complexvalued distributions) f such that the commutator operator Cf = [f,Δ] acting from H˙ 1(Rd ) to H˙ −1(Rd ). In other words, we give a complete solution to the problem for the boundedness of the Laplacian −Δ, which is fundamental to quantum mechanics. © 2005 Elsevier Inc. All rights reserved