The heat kernel and frequency localized functions on the Heisenberg group

2008/04/02 by Bahouri, Hajer, Gallagher, Isabelle · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0804.0340

Abstract

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 W^s,p spaces.

Cited by

• The Fujita exponent for a heat equation with mixed local and nonlocal nonlinearities on the Heisenberg group
• Cazenave-Dickstein-Weissler-type extension of Fujita's problem on Heisenberg groups

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