Geodesic
Limiting values of the Cauchy type integral in a~three-dimensional harmonic algebra
Eurasian mathematical journal, Tome 3 (2012) no. 2, pp. 120-128.

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We establish sufficient conditions for the existence of the limiting values of a certain analog of the Cauchy type integral taking values in a three-dimensional harmonic algebra with two-dimensional radical. 
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S. A. Plaksa; V. S. Shpakivskyi. Limiting values of the Cauchy type integral in a~three-dimensional harmonic algebra. Eurasian mathematical journal, Tome 3 (2012) no. 2, pp. 120-128. http://geodesic.mathdoc.fr/item/EMJ_2012_3_2_a7/

[1] N. A. Davydov, “The continuity of an integral of Cauchy type in a closed domain”, Doklady Akad. Nauk SSSR, 64:6 (1949), 759–762 (in Russian) | MR | Zbl

[2] F. D. Gakhov, Boundary Value Problems, Pergamon Press, Oxford, 1966 | MR | Zbl

[3] O. F. Gerus, “Finite-dimensional smoothness of Cauchy-type integrals”, Ukr. Math. J., 29:5 (1977), 490–493 | DOI | MR | Zbl

[4] O. F. Gerus, “On the modulus of continuity of solid derivatives of a Cauchy-type integral”, Ukr. Math. J., 50:4 (1998), 539–549 | DOI | MR | Zbl

[5] P. W. Ketchum, “Analytic functions of hypercomplex variables”, Trans. Amer. Math. Soc., 30:4 (1928), 641–667 | DOI | MR | Zbl

[6] K. S. Kunz, “Application of an algebraic technique to the solution of Laplace's equation in three dimensions”, SIAM J. Appl. Math., 21:3 (1971), 425–441 | DOI | MR | Zbl

[7] O. Lehto, K. I. Virtanen, Quasikonforme Abbildungen, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, 126, Springer-Verlag, Berlin–New York, 1965 | MR

[8] I. P. Mel'nichenko, “The representation of harmonic mappings by monogenic functions”, Ukr. Math. J., 27:5 (1975), 499–505 | DOI | MR

[9] I. P. Mel'nichenko, “Algebras of functionally invariant solutions of the three-dimensional Laplace equation”, Ukr. Math. J., 55:9 (2003), 1551–1559 | DOI | MR | Zbl

[10] I. P. Mel'nichenko, S. A. Plaksa, Commutative algebras and spatial potential fields, Inst. Math. NAS Ukraine, Kiev, 2008 (in Russian) | Zbl

[11] S. A. Plaksa, V. S. Shpakivskyi, On limiting values of Cauchy type integral in a harmonic algebra with two-dimensional radical, Preprint 2010.4, Inst. Math. NAS Ukraine, Kiev, 2010 (in Russian) | MR

[12] I. I. Privalov, Boundary properties of analytic functions, 2nd ed., GITTL, Moscow–Leningrad, 1950 (in Russian) | MR

[13] V. V. Salaev, “Direct and inverse estimates for a singular Cauchy integral along a closed curve”, Mat. Zametki, 19:3 (1976), 365–380 | MR | Zbl

[14] V. S. Shpakivskyi, S. A. Plaksa, “Integral theorems and a Cauchy formula in a commutative threedimensional harmonic algebra”, Bulletin Soc. Sci. et Lettr. Lódź, 60:2 (2010), 47–54 | MR | Zbl