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arXiv · 2302.12298

Sharpness of some Hardy-type inequalities

Lars-Erik Persson·Natasha Samko·George Tephnadze
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Abstract

The current status concerning Hardy-type inequalities with sharp constants is presented and described in a unified convexity way. In particular, it is then natural to replace the Lebesgue measure $dx$ with the Haar measure $dx/x.$ There are also derived some new two-sided Hardy-type inequalities for monotone functions, where not only the two constants are sharp but also where the involved function spaces are (more) optimal. As applications, a number of both well-known and new Hardy-type inequalities are pointed out. And, in turn, these results are used to derive some new sharp information concerning sharpness in the relation between different quasi-norms in Lorentz spaces.

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Lars-Erik Persson, Natasha Samko, George Tephnadze. 2023-02-18. Sharpness of some Hardy-type inequalities. https://arxiv.org/abs/2302.12298

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