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arXiv · 2610.33346

Optimal Non-Homogeneous Improvements of the Anisotropic Hardy Inequality

Giuseppina di Blasio·Giovanni Pisante·Georgios Psaradakis
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Abstract

We consider the Hardy inequality associated with a strongly convex Finsler norm $F$ on $\mathbb{R}^n$ and we study its optimal non-homogeneous improvements in the whole range $1 n$, proving in each regime that the logarithmic weights appear with the optimal exponents. In the borderline case $p=n$ this extends to general functions the optimal exponent previously known only for anisotropically radial functions. The proofs rely on a common ground-state reduction, combined with a splitting into an $F_o$-radial and a mean-free part for $1 n$.

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Giuseppina di Blasio, Giovanni Pisante, Georgios Psaradakis. 2026-10-23. Optimal Non-Homogeneous Improvements of the Anisotropic Hardy Inequality. https://arxiv.org/abs/2610.33346

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