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