Abstract
The aim of this work is to solve the Riemann boundary value problem on non-rectifiable curve. Its solvability depends on certain metric characteristics of the curve. We introduce new metric characteristics of dimensional type and new sharp conditions of solvability of the problem. In addition, we introduce and study a version of the Cauchy integral over non-rectifiable paths.
Mathematics Subject Classification (2000). Primary 30E25; secondary 46F10.
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Kats, B.A. (2012). The Riemann Boundary Value Problem on Non-rectifiable Curves and Fractal Dimensions. In: Ball, J., Curto, R., Grudsky, S., Helton, J., Quiroga-Barranco, R., Vasilevski, N. (eds) Recent Progress in Operator Theory and Its Applications. Operator Theory: Advances and Applications(), vol 220. Springer, Basel. https://doi.org/10.1007/978-3-0348-0346-5_8
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DOI: https://doi.org/10.1007/978-3-0348-0346-5_8
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