31 citations · 88 across the 10 of their papers we have counts for
12 papers
Muckenhoupt -properties of distance functions and applications to Hardy-Sobolev -type inequalities
Bartłomiej Dyda, Lizaveta Ihnatsyeva, Juha Lehrbäck +2
Let be a metric space equipped with a doubling measure. We consider weights , where is a closed set in and . We estab…
Self-improvement of uniform fatness revisited
Juha Lehrbäck, Heli Tuominen, Antti V. Vähäkangas
We give a new proof for the self-improvement of uniform p-fatness in the setting of general metric spaces. Our proof is based on rather standard methods of geometric analysis, and…
Removable singularities for div v = f in weighted Lebesgue spaces
Laurent Moonens, Emmanuel Russ, Heli Tuominen
Let be apositive weight. Assuming that a doubling condition and an Poincaré inequality on balls for the measure , as well as a growth conditio…
Approximation and quasicontinuity of Besov and Triebel-Lizorkin functions
Toni Heikkinen, Pekka Koskela, Heli Tuominen
We show that, for , , , Hajłasz-Besov and Hajłasz-Triebel-Lizorkin functions can be approximated in the norm by discrete median convolutions. This al…
Approximation by Hölder functions in Besov and Triebel-Lizorkin spaces
Toni Heikkinen, Heli Tuominen
In this paper, we show that Besov and Triebel-Lizorkin functions can be approximated by a Hölder continuous function both in the Lusin sense and in norm. The results are proven in…
Measure density and extension of Besov and Triebel-Lizorkin functions
Toni Heikkinen, Lizaveta Ihnatsyeva, Heli Tuominen
We show that a domain is an extension domain for a Hajłasz-Besov or for a Hajłasz-Triebel-Lizorkin space if and only if it satisfies a measure density condition. We use a modificat…
Regularity of the local fractional maximal function
Toni Heikkinen, Juha Kinnunen, Janne Korvenpää +1
This paper studies smoothing properties of the local fractional maximal operator, which is defined in a proper subdomain of the Euclidean space. We prove new pointwise estimates fo…
Fractional Hardy inequalities and visibility of the boundary
Lizaveta Ihnatsyeva, Juha Lehrbäck, Heli Tuominen +1
We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditio…
A pointwise characterization of functions of bounded variation on metric spaces
Panu Lahti, Heli Tuominen
We give a new characterization of the space of functions of bounded variation in terms of a pointwise inequality connected to the maximal function of a measure. The characterizatio…
Smoothing properties of the discrete fractional maximal operator on Besov and Triebel--Lizorkin spaces
Toni Heikkinen, Heli Tuominen
Motivated by the results of Korry and Kinnunen and Saksman, we study the behaviour of the discrete fractional maximal operator on fractional Hajlasz spaces, Hajlasz-Besov and Hajla…
Fractional maximal functions in metric measure spaces
Toni Heikkinen, Juha Lehrbäck, Juho Nuutinen +1
We study the mapping properties of fractional maximal operators in Sobolev and Campanato spaces in metric measure spaces. We show that, under certain restrictions on the underlying…
The equivalence between pointwise Hardy inequalities and uniform fatness
Riikka Korte, Juha Lehrbäck, Heli Tuominen
We prove an equivalence result between the validity of a pointwise Hardy inequality in a domain and uniform capacity density of the complement. This result is new even in Euclidean…