Norm Estimates of an Integral Operator in Topological Measure Spaces

Key Points

• This research aims to establish criteria for the boundedness and compactness of a Hardy-type integral operator in weighted Lebesgue spaces.
• Formulated criteria based on sequences influenced by weight functions and measures.
• Analyzed conditions under which compact operator ideals align with s-number sequences.
• Derivatives of operator norms were estimated using integral expressions tied to original weight functions.
• Developed new criteria that define boundedness and compactness for the integral operator.
• Identified specific conditions that link ideals of compact operators to the operator's s-number sequences.
• Obtained estimates of operator norms that reflect the underlying weight functions in the spaces.

Abstract