On some Noetherian criteria for singular integral operators with bounded coefficients

Key Points

• The aim is to establish Noetherian conditions for singular integral operators with specific properties regarding bounded coefficients.
• Analyzed singular integral operators with measurable and bounded coefficients.
• Conducted the study in spaces of integrable functions with specific weights.
• Assumed a piecewise smooth integration contour.
• Identified dependencies on the angle sizes at contour corner points.
• Established Noetherian conditions for the operators in certain function spaces.
• Demonstrated these conditions are necessary and sufficient for Lyapunov-type contours.
• Showed that the characteristics of the coefficients influence the Noetherian nature of the operators.

Abstract