Abstract
We consider the classical Riemann–Hilbert problem in a simply connected domain bounded by a piecewise smooth contour in the entire scale of weighted H¨older spaces. By using an appropriate refinement of the Kellogg theorem on a conformal mapping of this domain onto a disk, we provide a complete description of the solvability situation for this problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Muskhelishvili, N.I., Singulyarnye integral’nye uravneniya (Singular Integral Equations), Moscow: Nauka, 1968.
Soldatov, A.P., Odnomernye singulyarnye operatory i kraevye zadachi teorii funktsii (One-Dimensional Singular Operators and Boundary Value Problems in Function Theory), Moscow: Vyssh. Shkola, 1991.
Goluzin, G.M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo (Geometrical Theory of Functions of a Complex Variable), Moscow: Nauka, 1972.
Bitsadze, A.V., Osnovy teorii analiticheskikh funktsii (Foundations of the theory of Analytic Functions of a Complex Variable), Moscow: Nauka, 1984.
Aver’yanov, G.N. and Soldatov, A.P., Linear Conjugation Problem for Analytic Functions in a Family of Weighted Hölder Spaces, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 9, pp. 56–61.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © E.S. Meshcheryakova, A.P. Soldatov, 2016, published in Differentsial’nye Uravneniya, 2016, Vol. 52, No. 4, pp. 518–527.
Rights and permissions
About this article
Cite this article
Meshcheryakova, E.S., Soldatov, A.P. Riemann–Hilbert problem in a family of weighted Hölder spaces. Diff Equat 52, 495–504 (2016). https://doi.org/10.1134/S0012266116040091
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0012266116040091