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A new class of general refined Hardy-type inequalities with kernels (CROSBI ID 173555)

Prilog u časopisu | izvorni znanstveni rad

Čižmešija, Aleksandra ; Krulić, Kristina ; Pečarić, Josip A new class of general refined Hardy-type inequalities with kernels // Rad Hrvatske akademije znanosti i umjetnosti. Razred za matematičke, fizičke i kemijske znanosti. Matematičke znanosti, 17 (2013), 53-80

Podaci o odgovornosti

Čižmešija, Aleksandra ; Krulić, Kristina ; Pečarić, Josip

engleski

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

We state and prove a new class of re fined general Hardy-type inequalities related to the weighted Lebesgue spaces L^p and L^q, convex functions and integral operators. We also provide a class of new sufficient conditions for a weighted modular inequality to hold. As special cases of our results, we obtain refi nements of the classical one-dimensional Hardy's, Polya-Knopp's and Hardy-Hilbert's inequality and of related dual inequalities, as well as a generalization and re finement 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's inequality; Hardy-Hilbert's inequality; weights; power weights; convex functions; Hardy's operator; kernel

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Podaci o izdanju

17

2013.

53-80

objavljeno

1845-4100

Povezanost rada

Matematika