2 citations · 6 across the 3 of their papers we have counts for
5 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…
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…