Mappings of finite distortion: the degree of regularity (2009)
Daniel Faraco, Pekka Koskela, Xiao Zhong
This paper investigates the self-improving integrability properties of the so-called mappings of finite distortion. Let K(x) ≥ 1 be a measurable function defined on a domain Ω ⊂ R n, n ≥ 2,...
Koskela, Pekka, Yang, Dachun, Zhou, Yuan
In this paper, we establish the equivalence between the Haj{\l}asz-Sobolev spaces or classical Triebel-Lizorkin spaces and a class of grand Triebel-Lizorkin spaces on Euclidean spaces and also on...
Weighted pointwise Hardy inequalities (2009)
Koskela, Pekka, Lehrbäck, Juha
We introduce the concept of a visual boundary of a domain Ω ⊂ ℝn and show that the weighted Hardy inequality ∫Ω|u|p dΩβ−p ≤ C ∫Ω |∇u|pdΩβ, where dΩ(x) = dist(x, ∂Ω), holds...
LOCALLY UNIFORM DOMAINS AND QUASICONFORMAL MAPPINGS (2007)
Scientiarum Fennicae, David A. Herron, Pekka Koskela
Abstract. We document various properties of the classes of locally uniform and weakly linearly locally connected domains. We describe the boundary behavior for quasiconformal homeomorphisms of these...
Autoconfigurative Radio Networks (AuRa) (2007)
Frantti, Tapio, Jurvansuu, Marko, Mämmelä, Aarne, Alasalmi, Janne, Haataja, Ville, Juurakko, Suvi, ...
Communications Technologies. VTT's Research Programme 2002-2006. Final Report. Sipilä, Markku (ed.). VTT Publications 629, 119 - 122
Mäkelä, Jukka, Pentikousis, Kostas, Pääkkönen, Pekka, Kyllönen, Vesa, Korva, Jari, Majanen, Mikko, ...
Communications Technologies. VTT's Research Programme 2002-2006. Final Report. Sipilä, Markku (ed.). VTT Publications 629, 322 - 334
Pointwise characterizations of Hardy-Sobolev functions (2006)
We establish simple pointwise characterizations of functions in the Hardy-Sobolev spaces within the range n/(n+1)
Ends of metric measure spaces and Sobolev inequalities (2006)
Buckley, Stephen M., Koskela, Pekka
Generalizing work of Li and Wang, we prove sharp volume growth/decay rates for ends of metric measure spaces supporting a (p; p)-Sobolev inequality. A sharp result for (q; p)-Sobolev inequalities is...
Orlicz-Hardy inequalities (2004)
Buckley, Stephen M., Koskela, Pekka
We relate Orlicz-Hardy inequalities on a bounded Euclidean domain to certain fatness conditions on the complement. In the case of certain log-scale distortions of Ln, this relationship is necessary...
Mappings of finite distortion: Sharp Orlicz-conditions (2003)
Kauhanen, Janne, Koskela, Pekka, Malý, Jan, Onninen, Jani, Zhong, Xiao
We establish continuity, openness and discreteness, and the condition $(N)$ for mappings of finite distortion under minimal integrability assumptions on the distortion.
Mappings of finite distortion: Sharp Orlicz-conditions (2003)
Kauhanen, Janne, Koskela, Pekka, Malý, Jan, Onninen, Jani, Zhong, Xiao
We establish continuity, openness and discreteness, and the condition (N) for mappings of finite distortion under minimal integrability assumptions on the distortion.
Conformal metrics and size of the boundary (2002)
American Journal of Mathematics - Volume 124, Number 6, December 2002
Boundary behavior of quasi-regular maps and the isodiametric profile. (2001)
Hanson, Bruce, Koskela, Pekka, Troyanov, Marc
We study obstructions for a quasi-regular mapping $f:M\rightarrow N$of finite degree between Riemannian manifolds to blow up on or collapse on a non-trivial part of the boundary of $M$
Boundary behavior of quasi-regular maps and the isodiametric profile (2001)
Hanson, Bruce, Koskela, Pekka, Troyanov, Marc
We study obstructions for a quasi-regular mapping f : M -> N of finite degree between Riemannian manifolds to blow up on or collapse on a non-trivial part of the boundary of M.
Exceptional sets for the definition of quasiconformality (2000)
Kallunki, Sari., Koskela, Pekka.
American Journal of Mathematics - Volume 122, Number 4, August 2000
Sobolev met poincaré / Piotr Hajlasz, Pekka Koskela (2000)
"May 2000, volume 145, number 688 (first of 4 numbers)"
On the fusion problem for degenerate elliptic equations II (1999)
Buckley, Stephen M., Koskela, Pekka
Let F be a relatively closed subset of a Euclidean domain Ω. We investigate when solutions u to certain elliptic equations on Ω/F are restrictions of solutions on all of Ω. Specifically, we show...
Piotr Hajlasz, Sobolev Met Poincar'e, Sobolev Met Poincar'e, Pekka Koskela, Pekka Koskela
There are several generalizations of the classical theory of Sobolev spaces as they are necessary for the applications to Carnot-Carathéodory spaces, subelliptic equations, quasiconformal mappings...
Definitions of Sobolev classes on metric spaces (1998)
Bruno Franchi, Piotr Hajlasz, Bruno Franchi, Pekka Koskela, Pekka Koskela
There have been recent attempts to develop the theory of Sobolev spaces W 1;p on metric spaces that do not admit any differentiable structure. We prove that certain definitions are equivalent. We...
New Poincaré inequalities from old (1998)
Buckley, Stephen M., Koskela, Pekka
We discuss a geometric method, which we refer to as Coning, for generating new Poincar´e type inequalities from old ones. In particular, we derive weighted Poincaré inequalities for star-shaped...
Criteria for imbeddings of Sobolev-Poincaré type (1996)
Buckley, Stephen M., Koskela, Pekka
Our aim in this paper is to give geometrical characterizations of domains which support Sobolev-Poincaré type imbeddings.
Buckley, Stephen M., Koskela, Pekka, Lu, G.
In the abstract setting of homogeneous spaces, we prove the equivalence of two geometric conditions, namely the defining conditions for John domains and Boman domains.
Definitions of quasiconformality (1995)
Heinonen, Juha, Koskela, Pekka
We establish that the infinitesimal “ H -definition” for quasiconformal mappings on Carnot groups implies global quasisymmetry, and hence the absolute continuity on almost all lines. Our method...
Subelliptic Poincaré inequalities: the case p < 1 (1995)
Buckley, Stephen M., Koskela, Pekka, Lu, Guozhen
We obtain (weighted) Poincaré type inequalities for vector fields satisfying the Hörmander condition for $p
An inverse Sobolev lemma (1994)
We establish an inverse Sobolev lemma for quasiconformal mappings and extend a weaker version of the Sobolev lemma for quasiconformal mappings of the unit ball of Rn to the full range 0 < p < n. As...
Sobolev-Poincaré inequalities for p < 1 (1994)
Buckley, Stephen M., Koskela, Pekka
If Ω is a John domain (or certain more general domains), and |∇υ|a certain mild condition, we show that u Є W 1;1 loc (Ω) satisfies a Sobolev-Poincaré inequality (∫Ω|u – a|q)1/q ≤...
Sobolev mappings with integrable dilatations (1993)
Heinonen, Juha, Koskela, Pekka
We show that each quasi-light mapping f in the Sobolev space W 1 n ( Ω , R n ) satisfying ¦ Df ( x )¦ n ≦ K ( x, f ) J ( x, f ) for almost every x and for some K ε L r ( Ω ), r > n -1, is open...
Capacity extension domains / (1990)
Thesis (doctoral)--University of Jyväskylä, 1990.