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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

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Volume 7, Issue 4


Singular Integral Equations in Special Weighted Spaces

R. Duduchava
  • A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 1. M. Aleksidze St., Tbilisi 380093, Georgia. E-mail:
  • Other articles by this author:
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/ F.-O. Speck
  • Departamento de Matématica, Instituto Superior Técnico, U.T.L., Avenida Rovisco Pais, 1049-001 Lisboa, Portugal. E-mail:
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Published Online: 2010-02-23 | DOI: https://doi.org/10.1515/GMJ.2000.633


We prove the boundedness of the Cauchy singular integral operator in special weighted Sobolev and Hölder-Zygmund spaces for large values of the smoothness parameter, which is an integer m ≥ 0, when the underlying contour is piecewise-smooth with angular points and even with cusps. We obtain Fredholm criteria and an index formula for singular integral equations with piecewise-continuous coefficients and complex conjugation in the spaces and provided that the underlying contour has only angular points but no cusps. The Fredholm property and the index turn out to be independent of the smoothness parameter m.

Key words and phrases:: Cauchy singular integral equation; Fredholm property; Bessel potential space; Besov space; Sobolev space

About the article

Received: 2000-07-14

Published Online: 2010-02-23

Published in Print: 2000-12-01

Citation Information: Georgian Mathematical Journal, Volume 7, Issue 4, Pages 633–642, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/GMJ.2000.633.

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