On some Noetherian criteria for singular integral operators with bounded coefficients

Abstract

In this paper, Noetherian conditions are established for singular integral operators with measurable and bounded coefficients. The study is carried out in spaces of integrable functions with certain weights, and the integration contour is assumed to be piecewise smooth. The established Noetherian conditions depend on the space in which the research is carried out, on the coefficients of the operators, as well as on the sizes of the angles formed by the integration contour at its corner points. In the case of the Lyapunov-type contour, the presented Noetherian conditions are necessary and sufficient in which the operators studied are Noetherian.