On Hardy q-inequalities

2014/03/25 by Lech Maligranda, Maligranda, Lech, Ryskul Oinarov +3 · 1 citation
Mathematics · #Mathematical Inequalities and Applications #Differential Equations and Boundary Problems #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.1403.6292

Abstract

Some q-analysis variants of Hardy type inequalities of the form ∫₀^b (x^α-1 ∫₀^x t^-α f(t) d_qt)^p d_qx ≤ C ∫₀^b f^p(t) d_qt with sharp constant C are proved and discussed. A similar result with the Riemann-Liouville operator involved is also proved. Finally, it is pointed out that by using these techniques we can also obtain some new discrete Hardy and Copson type inequalities in the classical case.

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