55 citations · 230 across the 22 of their papers we have counts for
16 papers · 1 filter
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…
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\…
On density of compactly supported smooth functions in fractional Sobolev spaces
Bartłomiej Dyda, Michał Kijaczko
We describe some sufficient conditions, under which smooth and compactly supported functions are or are not dense in the fractional Sobolev space for an open, bounded…
On density of smooth functions in weighted fractional Sobolev spaces
Bartłomiej Dyda, Michał Kijaczko
We prove that smooth functions are dense in weighted fractional Sobolev spaces on an arbitrary open set, under some mild conditions on the weight. We also obtain a~simil…
Function spaces and extension results for nonlocal Dirichlet problems
Moritz Kassmann, Bartlomiej Dyda
We study function spaces and extension results in relation with Dirichlet problems involving integrodifferential operators. For such problems, data are prescribed on the complement…
Fractional Laplace operator and Meijer G-function
Bartłomiej Dyda, Alexey Kuznetsov, Mateusz Kwaśnicki
We significantly expand the number of functions whose image under the fractional Laplace operator can be computed explicitly. In particular, we show that the fractional Laplace ope…
Eigenvalues of the fractional Laplace operator in the unit ball
Bartłomiej Dyda, Alexey Kuznetsov, Mateusz Kwaśnicki
We describe a highly efficient numerical scheme for finding two-sided bounds for the eigenvalues of the fractional Laplace operator (-Delta)^{alpha/2} in the unit ball D in R^d, wi…
Regularity estimates for elliptic nonlocal operators
Bartlomiej Dyda, Moritz Kassmann
We study weak solutions to nonlocal equations governed by integrodifferential operators. Solutions are defined with the help of symmetric nonlocal bilinear forms. Throughout this w…
Hardy inequalities and non-explosion results for semigroups
Krzysztof Bogdan, Bartłomiej Dyda, Panki Kim
We prove non-explosion results for Schrödinger perturbations of symmetric transition densities and Hardy inequalities for their quadratic forms by using explicit supermedian functi…
On weighted Poincaré inequalities
Bartłomiej Dyda, Moritz Kassmann
The aim of this note is to show that Poincaré inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincaré inequalities are considered, too. T…
Comparability and regularity estimates for symmetric nonlocal Dirichlet forms
Bartłomiej Dyda, Moritz Kassmann
The aim of this work is to study comparability of nonlocal Dirichlet forms. We provide sufficient conditions on the kernel for local and global comparability. As an application we…
Fractional calculus for power functions
Bartłomiej Dyda
We calculate the fractional Laplacian for functions of the form and . As an application, we estimate the first eigenvalues of the fractional Lap…
The fractional Hardy inequality with a remainder term
Bartłomiej Dyda
We calculate the regional fractional Laplacian on some power function on an interval. As an application, we prove Hardy inequality with an extra term for the fractional Laplacian o…
The best constant in a fractional Hardy inequality
Krzysztof Bogdan, Bartłomiej Dyda
We prove an optimal Hardy inequality for the fractional Laplacian on the half-space.