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.
Back to talks