Singular Integrals with Flag Kernels on Homogeneous Groups: I
Alexander Nagel, Fulvio Ricci, Elias M. Stein, Stephen Wainger

TL;DR
This paper proves that convolution operators with flag kernels on homogeneous nilpotent Lie groups form an algebra and are bounded on L^p spaces, extending the understanding of singular integrals in this setting.
Contribution
It establishes the algebraic structure and boundedness of flag kernel operators on homogeneous groups, a significant advancement in harmonic analysis.
Findings
Operators form an algebra under composition.
Boundedness on L^p(G) for 1<p<∞.
Extension of singular integral theory to flag kernels.
Abstract
Let be a flag kernel on a homogeneous nilpotent Lie group . We prove that operators of the form form an algebra under composition, and that such operators are bounded on for .
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