19 citations · 54 across the 11 of their papers we have counts for
13 papers
Hardy-Sobolev-Maz'ya inequalities for
Avas Banerjee, Michał Kijaczko, Vivek Sahu
We establish Hardy--Sobolev--Maz'ya inequalities in the subquadratic range for singularities supported on affine subspaces and for arbitrary domains. We first prove a Hardy…
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 $$ \int_{\mathbb{R}^{d}_{+}}\int_{\mathbb{R}^…
Best constants for Hardy inequalities in Triebel--Lizorkin spaces
Michał Kijaczko
We find sharp constants in fractional Hardy inequalities for weighted Triebel--Lizorkin seminorms on the whole space and half-spaces. Our results generalize recently obtained weigh…
Weighted fractional Hardy-Sobolev and Hardy-Sobolev-Maz'ya inequalities with singularities on flat submanifold
Michał Kijaczko, Vivek Sahu
We investigate the sharp constant for weighted fractional Hardy inequalities with the singularity on a flat submanifold of codimension , where . We also prove a weigh…
Improved Hardy and Rellich inequalities for antisymmetric and odd functions
Michał Kijaczko
We investigate the Hardy and Rellich inequalities for classes of antisymmetric and odd functions and general exponent . The obtained constants are better than the classical ones…
Asymptotics of weighted Gagliardo seminorms
Michał Kijaczko
In this paper we consider fractional Sobolev spaces equipped with weights being powers of the distance to the boundary of the domain. We prove the versions of Bourgain--Brezis--Mir…
Shot-down stable processes
Krzysztof Bogdan, Kajetan Jastrzȩbski, Moritz Kassmann +2
The shot-down process is a strong Markov process which is annihilated, or shot down, when jumping over or to the complement of a given open subset of a vector space. Due to specifi…
Sharp fractional Hardy inequalities with a remainder for
Bartłomiej Dyda, Michał Kijaczko
The main purpose of this article is to obtain (weighted) fractional Hardy inequalities with a remainder and fractional Hardy-Sobolev-Maz'ya inequalities valid for .
Sharp weighted fractional Hardy inequalities
Bartłomiej Dyda, Michał Kijaczko
We investigate the weighted fractional order Hardy inequality $$ \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 Sobolev spaces with power weights
Michał Kijaczko
We investigate the form of the closure of the smooth, compactly supported functions in the weighted fractional Sobolev space for bounded .…
Sharp Hardy inequalities for Sobolev-Bregman forms
Michał Kijaczko, Julia Lenczewska
We obtain sharp fractional Hardy inequalities for the half-space and for convex domains. We extend the results of Bogdan and Dyda and of Loss and Sloane to the setting of Sobolev-B…
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…