In the Lieb-Loss's book , they present the Riesz rearrangement in Section3, Theorem 3.9(Page 93). Note that the functions f,g,h are all nonnegative. I want to ask whether the nonnegative condition can be removed, such as g(x)=-ln(x). Because in come cases, such as the fundamental solution of -\Delta in \mathbb{R}^2 is -ln x. In this cases, does the Riesz's Rearrangement inequality still holds?