18 citations · 40 across the 7 of their papers we have counts for
8 papers
Generalized Lebesgue points for Hajł asz functions
Toni Heikkinen
Let be a quasi-Banach function space over a doubling metric measure space . Denote by the generalized upper Boyd index of . We show that if an…
A median approach to differentiation bases
Toni Heikkinen, Juha Kinnunen
We study a version of the Lebesgue differentiation theorem in which the integral averages are replaced with medians over Busemann--Feller differentiation bases. Our main result giv…
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…
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…