The heat kernel and frequency localized functions on the Heisenberg group

الأصل · EN

The goal of this paper is to study the action of the heat operator on the Heisenberg group Hᵈ, and in particular to characterize Besov spaces of negative index on Hᵈ in terms of the heat kernel. That characterization can be extended to positive indexes using Bernstein inequalities. As a corollary we obtain a proof of refined Sobolev inequalities in Wˢ,ᵖ spaces.