engleski

A new class of general refined Hardy-type inequalities with kernels

We state and prove a new class of refined general Hardy-type inequalities related to the weighted Lebesgue spaces L^p and L^q, convex functions and the integral operators. As special cases of our results, we obtain refinements of the classical one-dimensional Hardy's, Polya-Knopp's, Hardy--Hilbert's and related dual inequalities, as well as a generalization and refinement of the classical Godunova's inequality. Finally, we show that our results may be seen as generalizations of some recent results related to Riemann-Liouville's and Weyl's operator.

Hardy inequality; Hardy-Hilbert inequality; weights; power weights; convex functions; Hardy operator; kernel.

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