206 citations · 394 across the 45 of their papers we have counts for
12 papers · 1 filter
Two-sided boundary points of Sobolev-extension domains on Euclidean spaces
Miguel García-Bravo, Tapio Rajala, Jyrki Takanen
We prove an estimate on the Hausdorff-dimension of the set of two-sided boundary points of general Sobolev-extension domains on Euclidean spaces. We also present examples showing l…
Dimension estimates for the boundary of planar Sobolev extension domains
Danka Lučić, Tapio Rajala, Jyrki Takanen
We prove an asymptotically sharp dimension upper-bound for the boundary of bounded simply-connected planar Sobolev -extension domains via the weak mean porosity of the bou…
Upper Conical density results for general measures on
Marianna Csörnyei, Antti Käenmäki, Tapio Rajala +1
We study conical density properties of general Borel measures on Euclidean spaces. Our results are analogous to the previously known result on the upper density properties of Hausd…
Packing dimension and Ahlfors regularity of porous sets in metric spaces
Esa Järvenpää, Maarit Järvenpää, Antti Käenmäki +3
Let be a metric measure space with an -regular measure . We prove that if is -porous, then where $\dim_{\math…
A geometric characterization of planar Sobolev extension domains
Pekka Koskela, Tapio Rajala, Yi Ru-Ya Zhang
We characterize bounded simply-connected planar -extension domains for as those bounded domains for which any two points $z_1,z_2 \in \ma…
A function whose graph has positive doubling measure
Tuomo Ojala, Tapio Rajala
We show that a doubling measure on the plane can give positive measure to the graph of a continuous function. This answers a question by Wang, Wen and Wen. Moreover we show that th…
Local multifractal analysis in metric spaces
Antti Käenmäki, Tapio Rajala, Ville Suomala
We study the local dimensions and local multifractal properties of measures on doubling metric spaces. Our aim is twofold. On one hand, we show that there are plenty of multifracta…
Thin and fat sets for doubling measures in metric spaces
Tuomo Ojala, Tapio Rajala, Ville Suomala
We consider sets in uniformly perfect metric spaces which are null for every doubling measure of the space or which have positive measure for all doubling measures. These sets are…
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…
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…
Packing dimension of mean porous measures
D. Beliaev, E. Järvenpää, M. Järvenpää +4
We prove that the packing dimension of any mean porous Radon measure on may be estimated from above by a function which depends on mean porosity. The upper bound tend…