On some applications of the essential norms of singular integral operators

Key Points

• The aim is to compute the norms and essential norms of singular integral operators and identify conditions for their equivalence.
• Calculated norms of singular operators using the Cauchy kernel.
• Determined conditions where norms coincide.
• Analyzed Noetherian properties in L₂ weighted spaces.
• Compared findings with established conditions of I. Simonenko.
• Essential norms and norms were calculated for singular operators.
• Identified conditions for equivalence of norms and essential norms.
• Established Noetherian properties under specific conditions for weighted coefficients.

Abstract