11 citations · 96 across the 32 of their papers we have counts for
13 papers · 1 filter
Existence and uniqueness of limits at infinity for homogeneous Sobolev functions
Pekka Koskela, Khanh Nguyen
We establish the existence and uniqueness of limits at infinity along infinite curves outside a zero modulus family for functions in a homogeneous Sobolev space under the assumptio…
Pointwise inequalities for Sobolev functions on outward cuspidal domains
Sylvester Eriksson-Bique, Pekka Koskela, Jan Maly +1
We show that the first order Sobolev spaces on cuspidal symmetric domains can be characterized via pointwise inequalities. In particular, they coincide with the Hajlasz-Sobolev spa…
Trace and density results on regular trees
Pekka Koskela, Khanh Ngoc Nguyen, Zhuang Wang
We give characterizations for the existence of traces for first order Sobolev spaces defined on regular trees.
Dyadic norm Besov-type spaces as trace spaces on regular trees
Pekka Koskela, Zhuang Wang
In this paper, we study function spaces defined via dyadic energies on the boundaries of regular trees. We show that correct choices of dyadic energies result in Besov-type spaces…
Sobolev extension via reflections
Pekka Koskela, ZhengZhu
We show that the extension results by Mazya and Poborchi for polynomial planar cusps can be realized via composition operators generated by reflections.
Product of extension domains is still an extension domain
Pekka Koskela, Zheng Zhu
We prove the product of the Sobolev-extension domains is still a Sobolev-extension domain.