Application of Interpolation Inequalities to the Study of Operators with Linear Fractional Endpoint Singularities in Weighted Hölder Spaces

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References

[1] Gakhov, F.D. (1977) Boundary Value Problems. Nauka, Moscow. (in Russian)

[2] Muskhelishvili, N.I. (2008) Singular Integral Equations, Boundary Value Problems of the Theory of Functions and Some of Their Applications to Mathematical Physics. Dover Publications, Mineola.

[3] Litvinchuk, G.S. (2000) Solvability Theory of Boundary Value Problems and Singular Integral Equations with Shift. Kluwer Academic Publishers, Dordrecht, Boston, London.

http://dx.doi.org/10.1007/978-94-011-4363-9

[4] Gohberg, I. and Krupnik, N. (1992) One-Dimensional Linear Singular Integral Equations. Operator Theory: Advances and Applications Vol. 53. Birkhauser Verlag, Basel, Boston, Berlin.

[5] Mikhlin, S.G. and Prossdorf, S. (1986) Singular Integral Operators. Akademie-Verlag, Berlin.

http://dx.doi.org/10.1007/978-3-642-61631-0

[6] Duduchava, R.V. (1963) Unidimensional Singular Integral Operator Algebras in Spaces of Holder Functions with Weight. Proceedings of A. Razmadze Mathematical Institute, 43, 19-52. (in Russian)

[7] Karapetiants, N.K. and Samko, S.G. (2001) Equations with Involutive Operator. Birkhauser Verlag, Boston, Basel, Berlin.

http://dx.doi.org/10.1007/978-1-4612-0183-0

[8] Duduchava, R.V. (1979) Convolution Integral Equations with Discontinuous Presymbols, Singular Integral Equations with Fixed Singularities and Their Applications to Problem in Mechanics. Proceedings of A. Razmadze Mathematical Institute, 60, 2-136. (in Russian)

[9] Karlovich, Yu. and Kravchenko, V. (1981) Singular Integral Equations with Non-Carleman Shift on an Open Contour. Differential Equations, 17, 1408-1417.

[10] Kravchenko, V.G. and Litvinchuk, G.S. (1994) Introduction to the Theory of Singular Integral Operators with Shift. Kluwer Academic Publishers, Dordrecht, Boston, London.

http://dx.doi.org/10.1007/978-94-011-1180-5

[11] Karelin, A. (1980) On a Boundary Value Problem with Shift for a System of Differential Equations of Elliptichyperbolic Type. Soviet Mathematics-Doklady, 22, 507-512.