@article{ZNSL_2018_467_a13,
author = {V. Ryazanov},
title = {The {Stieltjes} integrals in the theory of harmonic functions},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {151--168},
year = {2018},
volume = {467},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a13/}
}
V. Ryazanov. The Stieltjes integrals in the theory of harmonic functions. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 151-168. http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a13/
[1] N. K. Bari, A treatise on trigonometric series, v. I–II, Macmillan Co., New York, 1964 | MR
[2] A. A. Borovkov, Probability theory, Gordon and Breach Science Publishers, Amsterdam, 1998 | MR | Zbl
[3] O. Dovgoshey, O. Martio, V. Ryazanov, M. Vuorinen, “The Cantor function”, Expo. Math., 24 (2006), 1–37 | DOI | MR | Zbl
[4] P. L. Duren, Theory of $H^p$ spaces, Pure Appl. Math., 38, Academic Press, New York–London, 1970 | MR
[5] E. M. Dyn'kin, “Methods of the theory of singular integrals (the Hilbert transform and Calderón–Zygmund theory)”, Itogi Nauki i Tekhniki. Current problems in mathematics. Fundamental directions, 15, Moscow, 1987, 197–292 (in Russian) | MR | Zbl
[6] J. B. Garnett, D. E. Marshall, Harmonic Measure, Cambridge Univ. Press, Cambridge, 2005 | MR | Zbl
[7] F. W. Gehring, “On the Dirichlet problem”, Michigan Math. J., 3 (1955–1956), 201 | DOI | MR
[8] G. M. Goluzin, Geometric theory of functions of a complex variable, Transl. Math. Monographs, 26, 1969 | DOI | MR | Zbl
[9] V. P. Havin, “Boundary properties of integrals of Cauchy type and of conjugate harmonic functions in regions with rectifiable boundary”, Mat. Sb. (N.S.), 68(110):4 (1965), 499–517 (in Russian) | MR | Zbl
[10] P. L. Hennequin, A. Tortrat, Théorie des probabilités et quelques applications, Masson et Cie, Editeurs, Paris, 1965 | MR
[11] S. V. Kislyakov, “Classical problems of Fourier analysis”, Itogi Nauki i Tekhniki. Current problems in mathematics. Fundamental directions, 15, Moscow, 1987, 135–195 (in Russian) | MR | Zbl
[12] P. Koosis, Introduction to $H_p$ spaces, Cambridge Tracts in Mathematics, 115, 2nd ed., Cambridge Univ. Press, Cambridge, 1998 | MR | Zbl
[13] N. N. Luzin, “On the main theorem of integral calculus”, Mat. Sb., 28:2 (1912), 266–294 (in Russian) | Zbl
[14] N. N. Luzin, Integral and trigonometric series, Dissertation, Moscow, 1915 (in Russian) | MR
[15] N. N. Luzin, Integral and trigonometric series, Editing and commentary by N. K. Bari and D.E. Men'shov, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow–Leningrad, 1951 | MR
[16] N. Luzin, “Sur la notion de l'intégrale”, Ann. Mat. Pura Appl., 26:3 (1917), 77–129 | DOI
[17] D. Menchoff, “Sur la représentation des fonctions mesurables par des séries trigonométriques”, Rec. Math. [Mat. Sbornik] N.S., 9(51):3 (1941), 667–692 | MR | Zbl
[18] R. Nevanlinna, Eindeutige analytische Funktionen, Ann Arbor, Michigan, 1944 | MR
[19] W. F. Pfeffer, “Integration by parts for the generalized Riemann-Stieltjes integral”, J. Austral. Math. Soc. Ser. A, 34:2 (1983), 229–233 | DOI | MR | Zbl
[20] Ch. Pommerenke, Boundary behaviour of conformal maps, Fundamental Principles of Mathematical Sciences, 299, Springer–Verlag, Berlin, 1992 | MR | Zbl
[21] I. Privaloff, “Sur l'intégrale du type de Cauchy–Stieltjes”, Izvestia Akad. Nauk SSSR, Ser. Math., 4:3 (1940), 261–276 (in Russian) | MR | Zbl
[22] I. I. Priwalow, Introduction in the theory of functions of one complex variable, ed. 12, Nauka, Moscow, 1977 | MR
[23] I. I. Priwalow, Randeigenschaften analytischer Funktionen, Hochschulbücher für Mathematik, 25, Deutscher Verlag der Wissenschaften, Berlin, 1956 | MR | Zbl
[24] M. Riesz, “Sur les fonctions conjuguées”, Math. Z., 27 (1927), 218–244 | DOI | MR | Zbl
[25] V. Ryazanov, “On the Riemann-Hilbert problem without index”, Ann. Univ. Bucharest Ser. Math., 5(LXIII):1 (2014), 169–178 | MR | Zbl
[26] V. Ryazanov, “Infinite dimension of solutions of the Dirichlet problem”, Open Math. (the former Central European J. Math.), 13:1 (2015), 348–350 | MR | Zbl
[27] V. Ryazanov, “On the boundary behavior of conjugate harmonic functions”, Proceedings of Inst. Appl. Math. Mech. of Nat. Acad. Sci., 31, Ukraine, 2017, 117–123
[28] V. Ryazanov, Correlation of boundary behavior of conjugate harmonic functions, 3 Mar. 2018, 8 pp., arXiv: 1710.00323v3[math.CV]
[29] V. Ryazanov, A. Yefimushkin, “On the Riemann–Hilbert problem for the Beltrami equations”, Contemp. Math., 667 (2016), 299–316 | DOI | MR | Zbl
[30] S. Saks, Theory of the integral, Warsaw, 1937 ; Dover Publications Inc., New York, 1964 | Zbl | MR | Zbl
[31] V. Smirnoff, “Sur les valeurs limites des fonctions, régulières à l'interieur d'un cercle”, J. Soc. Phys.-Math. Léningrade, 2:2 (1929), 22–37 | MR | Zbl
[32] A. Zygmund, Trigonometric series, Wilno, 1935 | MR
[33] A. Yefimushkin, “On Neumann and Poincaré problems in $A$-harmonic analysis”, Advances in Analysis, 1:2 (2016), 114–120 ; (30 Aug. 2016), 14 pp., arXiv: 1608.08457v1[math.CV] | DOI | MR