Singular Integrals with Flag Kernels on Homogeneous Groups: I

2011/07/31 by Alexander Nagel, Nagel, Alexander, Fulvio Ricci +5
Mathematics · #42B20 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:42B20

paper · pdf · doi:10.48550/arxiv.1108.0177

92 pages

arxiv created 2011/07/31 · arxiv updated 2011/08/02

Abstract

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<∞.

Related

• Lp-boundedness of flag kernels on homogeneous groups
• Algebras of singular integral operators with kernels controlled by multiple norms
• Estimates for singular integrals on homogeneous groups
• Invertibility in the flag kernels algebra on the Heisenberg group
• Boundedness of oscillating singular integrals on Lie groups of polynomial growth