Invertibility in the flag kernels algebra on the Heisenberg group

2015/01/29 by Grzegorz Kępa, Kępa, Grzegorz
Mathematics · #Advanced Algebra and Geometry #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #math.FA

paper · pdf · doi:10.48550/arxiv.1501.07372

arxiv created 2015/01/29 · openalex publication_date 2015/01/29 · arxiv updated 2015/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Flag kernels are tempered distributions which generalize these of Calderon-Zygmund type. For any homogeneous group \mathbbG the class of operators which acts on L²(\mathbbG) by convolution with a flag kernel is closed under composition. In the case of the Heisenberg group we prove the inverse-closed property for this algebra. It means that if an operator from this algebra is invertible on L²(\mathbbG), then its inversion remains in the class.

Related

• Inverse-Closedness of a Banach Algebra of Integral Operators on the Heisenberg Group
• Invertibility of convolution operators on homogeneous groups
• Inverses of Product Kernels and Flag Kernels on Graded Lie Groups
• Singular Integrals with Flag Kernels on Homogeneous Groups: I
• Flag kernels of arbitrary order