Heat Kernels, Smoothness Estimates, and Exponential Decay

Albert Boggess, Andrew Raich

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


In this article, we characterize functions whose Fourier transforms have exponential decay. We characterize such functions by showing that they satisfy a family of estimates that we call quantitative smoothness estimates (QSE). Using the QSE, we establish Gaussian decay in the "bad direction" for the □b-heat kernel on polynomial models in ℂn+1. On the transform side, the problem becomes establishing QSE on a heat kernel associated to the weighted ∂̄-operator on L2(ℂ). The bounds are established with Duhamel's formula and careful estimation. In ℂ2, we can prove both on and off-diagonal decay for the □b-heat kernel on polynomial models.

Original languageEnglish (US)
Pages (from-to)180-224
Number of pages45
JournalJournal of Fourier Analysis and Applications
Issue number1
StatePublished - Feb 2013


  • Decoupled polynomial model
  • Gaussian decay
  • Heat kernel
  • Polynomial model
  • Quantitative smoothness estimates
  • Szegö kernel
  • Weighted ∂̄-operator

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Applied Mathematics


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