Singular Integrals with Flag Kernels on Homogeneous Groups: I

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

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classification 🧮 math.FA

keywords flagformhomogeneousmathcaloperatorsalgebraboundedcomposition

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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 $1<p<\infty$.

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Singular Integrals with Flag Kernels on Homogeneous Groups: I

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