Revista Matemática Iberoamericana


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Volume 28, Issue 3, 2012, pp. 631–722
DOI: 10.4171/RMI/688

Published online: 2012-07-16

Singular integrals with flag kernels on homogeneous groups, I

Alexander Nagel[1], Fulvio Ricci[2], Elias M. Stein[3] and Stephen Wainger[4]

(1) University of Wisconsin, Madison, USA
(2) Scuola Normale Superiore, Pisa, Italy
(3) Princeton University, United States
(4) University of Wisconsin at Madison, USA

Let $\mathcal K$ be a flag kernel on a homogeneous nilpotent Lie group $G$. We prove that operators $T$ of the form $T(f) = f*\mathcal K$ form an algebra under composition, and that such operators are bounded on $L^{p}(G)$ for $1 < p < \infty$.

Keywords: Flag kernel, homogeneous nilpotent Lie group, cancellation condition

Nagel Alexander, Ricci Fulvio, Stein Elias, Wainger Stephen: Singular integrals with flag kernels on homogeneous groups, I. Rev. Mat. Iberoamericana 28 (2012), 631-722. doi: 10.4171/RMI/688