31 citations · 88 across the 10 of their papers we have counts for
7 papers · 1 filter
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…
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…