
StatusThe thesis was presented on the 29 October, 2004Approved by NCAA on the 23 December, 2004 Abstract– 0.19 Mb / in romanian 
The dissertation is devoted to the following questions of the theory of singular integral operators: the calculation (and estimatin) of exact constants in theorems of M. Riss, B. Khvedelidze and I. Simonenko on the boundedness of operator with Cauchy kernel in different functional spaces, the application of these results to finding sufficient conditions of Noetherian properthy for systems of singular integral equations with bounded coefficients, the investigation of singular operators perturbed by some linear noncompact operators. The integration contour is assumed to have finitely many corner points.
To solve these problems in the work the local principle was adapted to the calculation of norms of operators of local type, whin made it possible instead of the norm of initial operator to calculate the norm of some simplest ”canonical” representatives at cach point of the contour. A rather wide class of functions that are weights relative to singular integrals in the space p L with weight was obtained. Basing on these results the estimates of essential norms for projecting M. Riss operators in the case of contour with corner points were found. It is proved that the essential norms of these operators depend on the space p L , on the weight and on the integration contour. A method is obtained that allows us to reduce the question about Noetherian property of a singular integral equation with bounded measurable coefficients in a Lesbegue space with weight to the investigation of Noetherian property of an analogous aquation in a space without weight. It is proved that for characteristic singular operators the Noetheran property is stable relative to their perturbation by some noncompact operators.
The methods and results of our dissertation can be used for further instigation of singular
integral operators and algebras generated by such operators; for application of such operators in the
theory of boundary value problems of mathematical physics; for solution of particular integral
equations in applied mathematics and other.