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math.AP2026
Fractional Hardy--Maz'ya inequality on a half-space
Michał Kijaczko, Antoni Szczukiewicz
The main purpose of this article is to provide a fractional counterpart of the well-known Maz'ya inequality on the half-space, that is $$ \int_{\mathbb{R}^{d}_{+}}\int_{\mathbb{R}^…
math.AP2026
Critical fractional Hardy inequalities
Krzysztof Bogdan, Bartłomiej Dyda, Antoni Szczukiewicz
We give a roadmap for the study of critical fractional Hardy inequalities for Dirichlet and Sobolev--Bregman forms. We focus on homogeneous forms on the real line, in particular th…