The Riemann Boundary Value Problem on Non-rectifiable Arcs and the Cauchy Transform

  • Boris A. KatsEmail author
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 221)


In this paper we introduce an alternative way of defining the curvilinear Cauchy integral over non-rectifiable arcs on the complex plane. We construct this integral as the convolution of the distribution (2πiz)-1 with a certain distribution such that its support is a non-rectifiable arc. These convolutions are called Cauchy transforms. As an application, solvability conditions of the Riemann boundary value problem are derived under very weak conditions on the boundary.


Non-rectifiable arc metric dimension Cauchy transform Riemann boundary value problem 


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Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Kazan Federal UniversityKazanRussia

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