Lp-boundedness of flag kernels on homogeneous groups
Pawel Glowacki
TL;DR
This paper proves that flag kernel singular integral operators on homogeneous groups are bounded on Lp spaces, using Littlewood-Paley theory and symbolic calculus, extending the understanding of harmonic analysis in this setting.
Contribution
It establishes Lp-boundedness of flag kernel operators on homogeneous groups, utilizing a novel combination of Littlewood-Paley theory and symbolic calculus.
Findings
Flag kernel operators are bounded on Lp spaces.
The natural gradation of the Lie algebra is key to the analysis.
The approach combines Littlewood-Paley theory with symbolic calculus.
Abstract
We prove that the flag kernel singular integral operators of Nagel-Ricci-Stein on a homogeneous group are bounded on the Lp spaces. The gradation associated with the kernels is the natural gradation of the underlying Lie algebra. Our main tools are the Littlewood-Paley theory and a symbolic calculus combined in the spirit of Duoandikoetxea and Rubio de Francia.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Mathematical Analysis and Transform Methods · advanced mathematical theories