55 citations · 230 across the 22 of their papers we have counts for
27 papers
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…
Fractional and non-fractional Hardy inequality on a lattice
Bartłomiej Dyda
We present simple proofs of a discrete fractional and non-fractional Hardy inequality, Our constants are explicit, but not optimal. In the class of power weights, we get a complete…
The Dirichlet Problem For the Logarithmic p-Laplacian
Bartłomiej Dyda, Sven Jarohs, Firoj Sk
We introduce and study the logarithmic -Laplacian , which emerges from the formal derivative of the fractional -Laplacian at . This operator is nonlo…
Sharp fractional Hardy inequalities with a remainder for
Bartłomiej Dyda, Michał Kijaczko
The main purpose of this article is to obtain (weighted) fractional Hardy inequalities with a remainder and fractional Hardy-Sobolev-Maz'ya inequalities valid for .
Sharp weighted fractional Hardy inequalities
Bartłomiej Dyda, Michał Kijaczko
We investigate the weighted fractional order Hardy inequality $$ \int_Ω\int_Ω\frac{|f(x)-f(y)|^{p}}{|x-y|^{d+sp}}\text{dist}(x,\partialΩ)^{-α}\text{dist}(y,\partialΩ)^{-β}\,dy\,dx\…
Fractional Poincaré and localized Hardy inequalities on metric spaces
Bartłomiej Dyda, Juha Lehrbäck, Antti V. Vähäkangas
We prove fractional Sobolev-Poincaré inequalities, capacitary versions of fractional Poincaré inequalities, and pointwise and localized fractional Hardy inequalities in a metric sp…