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A Bimonogenic Cauchy Transform on Higher Order Lipschitz Classes

  • Lianet De la Cruz Toranzo
  • Arsenio Moreno García
  • Tania Moreno García
  • Ricardo Abreu BlayaEmail author
  • Juan Bory Reyes
Article
  • 25 Downloads

Abstract

We prove that a Cauchy transform naturally arising for bimonogenic Clifford algebra valued functions theory behaves invariant on the higher order Lipschitz classes and obtain a Plemelj–Privalov theorem for the related singular integral transform. Moreover, we obtain an upper bound for the norm of such an operator in the pathological case of fractal boundaries.

Keywords

Cauchy transform Bimonogenic functions Higher order Lipschitz classes 

Mathematics Subject Classification

30G35 

Notes

Acknowledgements

We want to thank the referee whose generous and valuable remarks and comments brought improvements to the paper and enhance clarity.

J. Bory Reyes was partially supported by Instituto Politécnico Nacional in the framework of SIP programs.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Departamento Licenciatura en MatemáticaUniversidad de HolguínHolguínCuba
  2. 2.SEPI-ESIME-ZAC-Instituto Politécnico NacionalCiudad MéxicoMéxico

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