16 citations · 34 across the 19 of their papers we have counts for
20 papers
Median porosity is quasiconformally invariant
Tero Kilpeläinen, Antti V. Vähäkangas
A set in is median porous if the logarithm of its distance function has bounded mean oscillation. We show that this property is preserved under quasiconformal mappin…
Parabolic weak porosity and parabolic Muckenhoupt distance functions
Henri Lahdelma, Kim Myyryläinen, Antti V. Vähäkangas
We develop the parabolic weak porosity to characterize the parabolic Muckenhoupt weights with time-lag. Our main result shows that a nonempty closed set is parabolic weakly p…
Limits at infinity for Hajłasz-Sobolev functions in metric spaces
Angha Agarwal, Antti V. Vähäkangas
We study limits at infinity for homogeneous Hajlasz-Sobolev functions defined on uniformly perfect metric spaces equipped with a doubling measure. We prove that a quasicontinuous r…
Fractional Hardy inequalities and capacity density
Lizaveta Ihnatsyeva, Kaushik Mohanta, Antti V. Vähäkangas
We prove that a pointwise fractional Hardy inequality implies a fractional Hardy inequality, defined via a Gagliardo-type seminorm. The proof consists of two main parts. The first…
Classifying Triebel-Lizorkin capacities in metric spaces
Juha Lehrbäck, Kaushik Mohanta, Antti V. Vähäkangas
We study non-local or fractional capacities in metric measure spaces. Our main goal is to clarify the relations between relative Hajlasz-Triebel-Lizorkin capacities, potentional Tr…
Characterization of the upper Assouad codimension
Josh Kline, Antti V. Vähäkangas
We present a new notion, the upper Aikawa codimension, and establish its equivalence with the upper Assouad codimension in a metric space with a doubling measure. To achieve this r…
On the weighted inequality between the Gagliardo and Sobolev seminorms
Ritva Hurri-Syrjänen, Javier C. Martínez-Perales, Carlos Pérez +1
We prove weighted inequalities between the Gagliardo and Sobolev seminorms and also between the Marcinkiewicz quasi-norm and the Sobolev seminorm. With weights we improve ear…
On the BBM-phenomenon in fractional Poincaré-Sobolev inequalities with weights
Ritva Hurri-Syrjänen, Javier C. Martínez-Perales, Carlos Pérez +1
In this paper we unify and improve some of the results of Bourgain, Brezis and Mironescu and the weighted Poincaré-Sobolev estimate by Fabes, Kenig and Serapioni. More precisely, w…
The Hajłasz capacity density condition is self-improving
Javier Canto, Antti V. Vähäkangas
We prove a self-improvement property of a capacity density condition for a nonlocal Hajlasz gradient in complete geodesic spaces. The proof relates the capacity density condition w…
Hardy-Sobolev inequalities and weighted capacities in metric spaces
Lizaveta Ihnatsyeva, Juha Lehrbäck, Antti V. Vähäkangas
Let be an open set in a metric measure space . Our main result gives an equivalence between the validity of a weighted Hardy-Sobolev inequality in and quasiadditivity of…
Self-improvement of pointwise Hardy inequality
Sylvester Eriksson-Bique, Antti V. Vähäkangas
We prove the self-improvement of a pointwise -Hardy inequality. The proof relies on maximal function techniques and a characterization of the inequality by curves.
Fractional Hardy-Sobolev type inequalities for half spaces and John domains
Bartłomiej Dyda, Juha Lehrbäck, Antti V. Vähäkangas
As our main result we prove a variant of the fractional Hardy-Sobolev-Maz'ya inequality for half spaces. This result contains a complete answer to a recent open question by Musina…
In between the inequalities of Sobolev and Hardy
Juha Lehrbäck, Antti V. Vähäkangas
We establish both sufficient and necessary conditions for the validity of the so-called Hardy-Sobolev inequalities on open sets of the Euclidean space. These inequalities form a na…
Fractional Sobolev-Poincaré and fractional Hardy inequalities in unbounded John domains
Ritva Hurri-Syrjänen, Antti V. Vähäkangas
We prove fractional Sobolev-Poincaré inequalities in unbounded John domains and we characterize fractional Hardy inequalities there.
Non-Homogeneous Local Theorem: Dual Exponents
Michael T. Lacey, Antti V. Vähäkangas
We provide an alternative proof of a (local) T1 theorem for dual exponents in the non-homogeneous setting of upper doubling measures. This previously known theorem provides necessa…
Hardy inequalities in Triebel-Lizorkin spaces
Lizaveta Ihnatsyeva, Antti V. Vähäkangas
We prove an inequality of Hardy type for functions in Triebel-Lizorkin spaces. The distance involved is being measured to a given Ahlfors d-regular set in R^n, with n-1<d<n. As an…
The local non-homogeneous Tb theorem for vector-valued functions
Tuomas P. Hytönen, Antti V. Vähäkangas
We extend the local non-homogeneous Tb theorem of Nazarov, Treil and Volberg to the setting of singular integrals with operator-valued kernel that act on vector-valued functions. H…
On fractional Poincaré inequalities
Ritva Hurri-Syrjänen, Antti V. Vähäkangas
We show that fractional (p,p)-Poincaré inequalities and even fractional Sobolev-Poincaré inequalities hold for bounded John domains, and especially for bounded Lipschitz domains. W…
A T1 theorem for weakly singular integral operators
Antti V. Vähäkangas
We establish conditions in the spirit of the T1 theorem of David and Journé which guarantee the boundedness of \nabla T on L^p(\R^n), where T is an integral transformation and 1<p<…
On extension of Green's operator on bounded smooth domains
Antti Vähäkangas
We prove a regularity result for Green's functions that are associated to elliptic second order divergence-type linear PDO's with coefficients in C^{1,α}(\barΩ). Here α\in (0,1) an…