99 citations · 316 across the 39 of their papers we have counts for
47 papers
Critical discrete Hardy inequalities in
Krzysztof Bogdan, Shubham Gupta, Kamil Kaleta +1
We establish ground-state representations and critical Hardy inequalities in the discrete setting. In particular, we construct critical Hardy weights for the discrete Dirichl…
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…
Subordinated Bessel heat kernels
Krzysztof Bogdan, Konstantin Merz
We prove new bounds for Bessel heat kernels and Bessel heat kernels subordinated by stable subordinators. In particular, we provide a 3G inequality in the subordinated case.
Self-similar solution for fractional Laplacian in cones
Krzysztof Bogdan, Piotr Knosalla, Łukasz Leżaj +1
We construct a self-similar solution of the heat equation for the fractional Laplacian with Dirichlet boundary conditions in every fat cone. As applications, we give the Yaglom lim…
Ground state representation for the fractional Laplacian with Hardy potential in angular momentum channels
Krzysztof Bogdan, Konstantin Merz
Motivated by the study of relativistic atoms, we consider the Hardy operator acting on functions of the form in $L^2(\m…
Positive harmonically bounded solutions for semi-linear equations
Wolfhard Hansen, Krzysztof Bogdan
For open sets in some space , we are interested in positive solutions to semi-linear equations on . Here may be an elliptic or parabolic operator of…