Reduction theorems for weighted integral inequalities on the cone of monotone functions

A. Gogatishvili   ; V. D. Stepanov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 68 (2013) no. 4, pp. 597-664

Résumé

This paper surveys results related to the reduction of integral inequalities involving positive operators in weighted Lebesgue spaces on the real semi-axis and valid on the cone of monotone functions, to certain more easily manageable inequalities valid on the cone of non-negative functions. The case of monotone operators is new. As an application, a complete characterization for all possible integrability parameters is obtained for a number of Volterra operators. Bibliography: 118 titles.

Détail

Keywords: weighted Lebesgue space, cone of monotone functions, duality principle, weighted integral inequality, bounded operators, reduction theorem.

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