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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1986 Jan;83(1):1–3. doi: 10.1073/pnas.83.1.1

Oscillatory singular integrals and harmonic analysis on nilpotent groups

F Ricci †, E M Stein ‡
PMCID: PMC322778  PMID: 16593640

Abstract

Several related classes of operators on nilpotent Lie groups are considered. These operators involve the following features: (i) oscillatory factors that are exponentials of imaginary polynomials, (ii) convolutions with singular kernels supported on lower-dimensional submanifolds, (iii) validity in the general context not requiring the existence of dilations that are automorphisms.

Keywords: Calderón-Zygmund kernels, nonautomorphic dilations

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Phong D. H., Stein E. M. Singular integrals related to the Radon transform and boundary value problems. Proc Natl Acad Sci U S A. 1983 Dec;80(24):7697–7701. doi: 10.1073/pnas.80.24.7697. [DOI] [PMC free article] [PubMed] [Google Scholar]

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