Bartłomiej Dyda

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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…

math.AP2025

The Dirichlet Problem For the Logarithmic p-Laplacian

BartÅomiej Dyda, Sven Jarohs, Firoj Sk

We introduce and study the logarithmic $p$ -Laplacian $L_{I^_{p}}$ , which emerges from the formal derivative of the fractional $p$ -Laplacian $(- I^_{p})^{s}$ at $s = 0$ . This operator is non…