Nazarbay Bliev
Singular integral operators in the Besov spaces
Abstract.
The properties of Cauchy type integral and corresponding singular integrals with Cauchy kernel along Lyapunov's contour are studied in the class of continuous (not exactly Holder -- continuous) functions in terms o the Besov spaces. For corresponding singular integral equations Noether's theorems are established. Besides elliptical operators we are studied the case with broken condition of ellipticity (normality) in finite number of points on contour, vanishing to zeros of integer orders. The Fredholm conditions of investigated operators are obtained and the spaces of Noetherian are indicated.
References
1. Bliev N.K. Generalized analytic functions in fractional spaces, USA: Longman, 1997, 145 pp.
2. O.V. Besov, V.P. Il'in, S.M. Nikol'ckii: Integral representations of functions and embedding theorems, 1, 2. John Willey. New York, 1978;1979, 345; 399 pp.

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