科研之友
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摘要
By using the notion of the subdifferential of a convex function, we state and prove a new general refined weighted Hardy-type inequality for convex functions and the integral operator with a non-negative kernel. We point out that the obtained result generalizes and refines the classical one-dimensional Hardy's, Polya-Knopp's, and Hardy-Hilbert's inequalities, as well as related dual inequalities. We show that our results may be seen as generalizations of some recent results related to Riemann-Liouville's and Weyl's operator, as well as a generalization and a refinement of the so-called Godunova's inequality.
- 出版日期2010-12
