The form boundedness criterion for the Laplacian operator

[摘要] In this paper, we characterize the class of measurable functions (or, more generally, real- or complex-valued distributions) f such that the commutator operator C-f = [f, Delta] acting from H-1(R-d) to H-1(R-d). In other words, we give a complete solution to the problem for the boundedness of the Laplacian -Delta, which is fundamental to quantum mechanics. (c) 2005 Elsevier Inc. All rights reserved.

[发布日期] 2006-11-15

[关键词] commutator;multipliers spaces;Sobolev space