Sharp Hardy inequalities for Sobolev-Bregman forms

We obtain sharp fractional Hardy inequalities for the half-space and for convex domains. We extend the results of Bogdan and Dyda and of Loss and Sloane to the setting of Sobolev-Bregman forms.

💡 Research Summary

The paper establishes sharp fractional Hardy inequalities for Sobolev‑Bregman forms in the half‑space and for general convex domains, extending earlier results of Bogdan‑Dyda and Loss‑Sloane to a nonlinear, p‑dependent setting.

Let (0<\alpha<2), (d\in\mathbb N) and (1<p<\infty). For a function (u:\mathbb R^{d}\to\mathbb R) with compact support in the half‑space (D={x\in\mathbb R^{d}:x_{d}>0}) the authors define the Sobolev‑Bregman energy
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