206 citations · 394 across the 45 of their papers we have counts for
5 papers · 1 filter
Existence of doubling measures via generalised nested cubes
Antti Käenmäki, Tapio Rajala, Ville Suomala
Working on doubling metric spaces, we construct generalised dyadic cubes adapting ultrametric structure. If the space is complete, then the existence of such cubes and the mass dis…
Generalized Hausdorff dimension distortion in Euclidean spaces under Sobolev mappings
Tapio Rajala, Aleksandra Zapadinskaya, Thomas Zürcher
We investigate how the integrability of the derivatives of Orlicz-Sobolev mappings defined on open subsets of affect the sizes of the images of sets of Hausdorff dim…
Generalized Dimension Distortion under Mappings of Sub-Exponentially Integrable Distortion
Tapio Rajala, Aleksandra Zapadinskaya, Thomas Zürcher
We prove a dimension distortion estimate for mappings of sub-exponentially integrable distortion in Euclidean spaces, which is essentially sharp in the plane.
Local homogeneity and dimensions of measures
Antti Käenmäki, Tapio Rajala, Ville Suomala
We introduce two new concepts, local homogeneity and local L^q-spectrum, both of which are tools that can be used in studying the local structure of measures. The main emphasis is…
Weakly controlled Moran constructions and iterated functions systems in metric spaces
Tapio Rajala, Markku Vilppolainen
We study the Hausdorff measures of limit sets of weakly controlled Moran constructions in metric spaces. The separation of the construction pieces is closely related to the Hausdor…