Singular integrals with flag kernels on homogeneous groups, I

Alexander Nagel; Fulvio Ricci; Elias M. Stein; Stephen Wainger

doi:10.4171/rmi/688

JournalsrmiVol. 28, No. 3pp. 631–722

Singular integrals with flag kernels on homogeneous groups, I

Alexander Nagel
University of Wisconsin, Madison, USA
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Fulvio Ricci
Scuola Normale Superiore, Pisa, Italy
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Elias M. Stein
Princeton University, United States
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Stephen Wainger
University of Wisconsin at Madison, USA
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Abstract

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

Cite this article

Alexander Nagel, Fulvio Ricci, Elias M. Stein, Stephen Wainger, Singular integrals with flag kernels on homogeneous groups, I. Rev. Mat. Iberoam. 28 (2012), no. 3, pp. 631–722

DOI 10.4171/RMI/688