This is a preview of subscription content, log in via an institution to check access.
Literature cited
I. I. Danilyuk, Nonregular Boundary Value Problems in the Plane [in Russian], Nauka, Moscow (1975).
I. I. Privalov, Boundary Properties of Analytic Functions [in Russian], GITTL, Moscow-Leningrad (1950).
A. P. Calderon, “Cauchy integrals on Lipschitz curves and related operators,” Proc. Nat. Acad. U.S.A.,74, No. 4, 1324–1327 (1977).
W. Rudin, Functional Analysis, New York (1973).
A. A. Gonchar and L. D. Grigoryan, “On estimates of the norm of the holomorphic constituents of a meromorphic function,” Mat. Sb.,99, No. 4, 634–638 (1976).
L. D. Grigoryan, “Estimates of the norm of the holomorphic constituents of meromorphic functions in domains with smooth boundary,” Mat. Sb.,100, No. 1, 156–164 (1976).
R. Takenaka, “On the orthogonal functions and a new formula of interpolation,” Jpn. J. Math.,2, 129–145 (1925).
M. M. Dzhrbashyan, “A contribution to the theory of Fourier series in rational functions,” Izv. Akad. Nauk Arm. SSR, Ser. Mat.,9, No. 7, 3–28 (1956).
A. Kh. Turetskii, The Theory of Interpolation in Problems. Part 2 [in Russian], Vyshchéishaya Shkola, Minsk (1977).
G. Ts. Tumarkin, “Expansion of analytic functions in series of rational functions with a given set of poles,” Izv. Akad. Nauk Arm. SSR, Ser. Mat.,14, No. 1, 9–31 (1961).
E. M. Dyn'kin, “On uniform approximation of functions in Jordan domains,” Sib. Mat. Zh.,18, No. 4, 775–786 (1977).
J. L. Walsh, Interpolation and Approximation by Rational Functions in the Complex Domain, Am. Math. Soc. (1966).
J. Schur, “Uber Potenzreihen, die im Innern des Einheitskrises beschrankt sind,” J. Reine Angew. Math.,147, 205–232 (1917).
A. A. Pekarskii, “Rational approximation and Orlicz spaces,” Dep. VINITI, No. 314–78.
A. A. Pekarskii, “Rational approximation of continuous functions with given modulus of continuity and modulus of variation,” Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat., No. 5, 34–39 (1978).
V. A. Popov, “Uniform rational approximation of the class Vr and its applications,” Acta Math. Acad. Sci. Hung.,29, 119–129 (1977).
V. A. Popov and P. P. Petrushev, “Sharp order of best uniform approximation of convex functions by rational functions,” Mat., Sb.,103, No. 2, 285–292 (1977).
E. P. Dolzhenko, “Rational approximation and boundary properties of analytic functions,” Mat., Sb.,69, No. 4, 498–528 (1966).
E. A. Sevast'yanov, “Rational approximation and absolute convergence of Fourier series,” Mat., Sb.,107, No. 2, 227–244 (1978).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 31, No. 3, pp. 389–402, March, 1982.
In conclusion the author expresses his gratitude to the referee, whose comments improved the exposition of the problems discussed here.
Rights and permissions
About this article
Cite this article
Pekarskii, A.A. Estimates of the derivative of a Cauchy-type integral with meromorphic density and their applications. Mathematical Notes of the Academy of Sciences of the USSR 31, 199–206 (1982). https://doi.org/10.1007/BF01145468
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01145468