References
- Gakhov FD. Boundary value problems. Moscow: Nauka Publishers; 1977.
- Muskhelishvili NI. Singular integral equations. Moscow: Nauka Publishers; 1962.
- Lu J-K. Boundary value problems for analytic functions. Singapore: World Scientific; 1993.
- Kats BA. Riemann boundary value problem on non-rectifiable Jordan curve. Doklady AN USSR. 1982;267(4):789–792.
- Kats BA. Riemann problem on closed Jordan curve. Izvestiya Vuzov Matem. 1983;4:68–80.
- Kats BA. Riemann problem on non-closed Jordan curve. Izvestiya Vuzov Matem. 1983;12:30–38.
- Kats BA. On inhomogeneous Riemann problem on non-closed Jordan curve. Trudy Semin. Po Kraevym Zadacham Kazan Univ. 1984;21:87–93.
- Falconer KJ. Fractal geometry. 3rd ed. Chichester: Wiley and Sons; 2014.
- Tricot C. Curves and fractal dimension. New York: Springer-Verlag; 1995.
- Dyn'kin EM. Smoothness of the Cauchy-type integrals. Zapiski Nauchn Semin LOMI AN USSR. 1979;92:115–133.
- Salimov T. Direct bound for the Cauchy singular integral over closed curve. Nauchn, Trudy MV I SSO Azerb SSR. 1979;5:59–75.
- Kats BA, Katz DB. Marcinkiewicz exponents and integrals over non-rectifiable paths. Math Meth Appl Sci. 2016;39(12):3402–3410.
- Kats BA. On integration over non-rectifiable path. Moscow. Inzh.–Stroit. Inst. Voprosy Matem., Mechan. Splosh. Sred i Primen. Matem. Metodov v Stroit. Sbornik Nauchn. Trudov. Moscow: MISI; 1982. p. 63–69.
- Abreu-Blaya R, Bory-Reyes J, Kats BA. Integration over non-rectifiable curves and Riemann boundary value problems. J–Math Anal Appl. 2011;380(1):177–187.
- Abreu-Blaya R, Bory-Reyes J, Kats BA. The Cauchy-type integral and singular integral operator over closed Jordan curves. Monatshefte Fur Mathematik. 2015;176(1):1–15.
- Guseynov Y. Integrable boundaries and fractals for Holder classes; the Gauss-Green theorem. Calc Var Partial Differ Equ. 2016;55(4):1–27.
- Harrison J, Norton A. Geometric integration on fractal curves in the plane. Indiana Univ Math J. 1991;40(2):567–594.
- Harrison J, Norton A. The Gauss-Green theorem for fractal boundaries. Duke Math J. 1992;67(3):575–588.
- Harrison J. Lectures on chainlet geometry – new topological methods in geometric measure theory. Proceedings of Ravello Summer School for Mathematical; 24 May 2005. arXiv:math-ph/0505063v1.
- Kats BA. The Cauchy integral along Φ-rectifiable curves. Lobatchevskii J Math. 2000;7:15–29.
- Kats BA. The inequalities for polynomials and integration over fractal arcs. Canadian Math Bull. 2001;44(1):61–69.
- Kats BA. The Cauchy integral over non-rectifiable paths. Contemporary Math. 2008;455:183–196.
- Kats BA. The Cauchy transform of certain distributions with application. Complex Anal Oper Theor. 2012;6(6):1147–1156.
- Kats BA. The Riemann boundary value problem on non-rectifiable curves and related questions. Complex Var Elliptic Equ. 2014;59(8):1053–1069.
- Katz DB, Kats BA. Interactions of germs with applications. Mathematical methods in applied sciences. On-line publication 22 February 2017 DOI: https://doi.org/10.1002/mma.4362.
- Kats BA, Katz DB. Integration over nonrectifiable paths with applications. Siberian Math J. 2019;60(1):71–81. DOI: https://doi.org/10.1134/S0037446619010087
- Kats BA, Katz DB. Curvilinear integrals of discontinuous functions over non-rectifiable paths and Riemann boundary-Value problem. Math Meth Appl Sci. 2019;42(6):1795–1803. Available From: http//dol.org/https://doi.org/10.1002//mma.5474
- Stein EM. Singular integrals and differential properties of functions. Princeton: Princeton University Press; 1970.
- Katz D. The Marcinkiewicz exponent with applications. ISAAC 9th congress; Krakow: 2013. p. 106–107.
- Dolzhenko EP. On ‘erazing’ of singularities of analytic functions. Uspekhi Matem Nauk. 1963;18(4):135–142.
- Vekua IN. Generalized analytical functions. Moscow: Nauka; 1988.
- Liu H. A note about Riemann boundary value problems on non-rectifiable curves. Complex Var Elliptic Equ. 2007;52(10–11):877–882.
- Kats BA, Katz DB. Cauchy – Hadamard integral with applications. Monatschefte Fur Matematik. 2019;189(4):683–689. DOI https://doi.org/10.1007/s00605-019-01263-z
- Kats BA. Zigzags and spirals in boundary-value problems. Izvestija Vuzov Matem. 2019;7:39–47. DOI: https://doi.org/10.26907/0021-3446-2019-7-39-47
- Rudin W. Real and complex analysis. New York: McGraw-Hill; 1987.