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The Heat Kernel and Frequency Localized Functions on the Heisenberg Group

2009; Linguagem: Inglês

10.1007/978-0-8176-4861-9_2

2374-0280

Hajer Bahouri, Isabelle Gallagher,

Mathematical Analysis and Transform Methods

The goal of this paper is to study the action of the heat operator on the Heisenberg group H d , and in particular to characterize Besov spaces of negative index on H d 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 $$\dot W^{s,p}$$ spaces.