2 citations · 2 across the 3 of their papers we have counts for
7 papers
The Variation of the Fractional Maximal Function of a Radial Function
Hannes Luiro, José Madrid
In this paper we study the regularity of the non-centered fractional maximal operator . As the main result, we prove that there exists such that if and $f…
The variation of the maximal function of a radial function
Hannes Luiro
We study the problem concerning the variation of the Hardy-Littlewood maximal function in higher dimensions. As the main result, we prove that the variation of the non-centered Har…
Gradient walk and -harmonic functions
Hannes Luiro, Mikko Parviainen
We consider a class of stochastic processes and establish its connection to -harmonic functions. In particular, we obtain stochastic approximations that converge uniformly to a…
Beyond local maximal operators
Hannes Luiro, Antti V. Vähäkangas
We obtain (essentially sharp) boundedness results for certain generalized local maximal operators between fractional weighted Sobolev spaces and their modifications. Concrete bound…
On the uniqueness of quasihyperbolic geodesics
Hannes Luiro
In this work we solve a couple of well known open problems related to the quasihyperbolic metric. In the case of planar domains, our first main result states that quasihyperbolic g…
On the existence and uniqueness of p-harmonious functions
Hannes Luiro, Mikko Parviainen, Eero Saksman
We give a self-contained and short proof for the existence, uniqueness and measurability of so called -harmonious functions. The proofs only use elementary analytic tools. As a…