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Journal of Fourier Analysis and Applications

, Volume 22, Issue 5, pp 1076–1096 | Cite as

Invertibility in the Flag Kernels Algebra on the Heisenberg Group

  • Grzegorz KępaEmail author
Article

Abstract

Flag kernels are tempered distributions which generalize these of Calderón–Zygmund type. For any homogeneous group \(\mathbb {G}\) the class of operators which acts on \(L^{2}(\mathbb {G})\) 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 \(L^{2}(\mathbb {G})\), then its inversion remains in the class.

Keywords

Flag kernel Heisenberg group Inverse-closed 

Mathematics Subject Classification

42B15 42B20 

Notes

Acknowledgments

The author wishes to express his deep gratitude to P.Głowacki and M.Preisner for their helpful advices in preparing the manuscript.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of WrocławWrocławPoland

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