Lorentz Spaces and Lie Groups Original Research Article

This paper is motivated by the behavior of the heat diffusion kernelpt(x) on a general unimodular Lie group. Indeed, contrary to what happens in Rn:, thePt(x) on a general Lie group is behaving liket−δ(t)/2for two possibly distinct integersδ(t), one forttending to 0 and another forttending to ∞, namelydandD. This forces us to consider a natural generalization of Lorentz spaces with different indices at “zero” and at “infinity.”