engleski

Some new refined Hardy-Type inequalities with kernels

In this talk we state and prove a new general refined, weighted Hardy-type inequality for convex functions and integral operator. We point out that the obtained result generalizes and refines the classical one-dimensional Hardy, Polya-Knopp's, Hardy-Hilbert inequalities, related dual inequalities, as well as their multidimensional analogues for cones in R.Moreover, we show that our relations may be seen as generalizations of some new recent results related to Riemann-Liouville's operator. Finally, we obtain some new refined Hardy-type inequalities for sequence of non-negative real numbers.

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

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