Three weights higher order Hardy type inequalities

Aigerim Aisultankyzy Kalybay, Lars‐Erik Persson

Journal of Function Spaces, 2006

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DOI 10.1155/2006/578175

Data confidence 70 medium

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Abstract

We investigate the following three weights higher order Hardy type inequality (0.1) where denotes the following weighted differential operator: for a weight function ρ(·). A complete description of the weights u, v and ρ so that (0.1) holds was given in [4] for the case 1 < p ≤ q < 8. Here the corresponding characterization is proved for the case 1 < q < p < 8. The crucial step in the proof of the main result is to use a new Hardy type inequality (for a Volterra type operator), which we first state and prove.