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• Assouad Type Dimensions in Geometric Analysis 

  Lehrbäck, Juha (Birkhäuser, 2021)

  We consider applications of the dual pair of the (upper) Assouad dimension and the lower (Assouad) dimension in analysis. We relate these notions to other dimensional conditions such as a Hausdorff content density condition ...

• On Limits at Infinity of Weighted Sobolev Functions 

  Eriksson-Bique, Sylvester; Koskela, Pekka; Nguyen, Khanh (Elsevier, 2022)

  We study necessary and sufficient conditions for a Muckenhoupt weight w∈Lloc1(Rd) that yield almost sure existence of radial, and vertical, limits at infinity for Sobolev functions u∈Wloc1,p(Rd,w) with a p-integrable ...

• Assouad Dimension, Nagata Dimension, and Uniformly Close Metric Tangents 

  Le Donne, Enrico; Rajala, Tapio (Indiana University, 2015)

  We study the Assouad dimension and the Nagata dimension of metric spaces. As a general result, we prove that the Nagata dimension of a metric space is always bounded from above by the Assouad dimension. Most of the paper ...

• Hardy inequalities and Assouad dimensions 

  Lehrbäck, Juha (Hebrew University Magnes Press; Springer, 2017)

  We establish both sufficient and necessary conditions for weighted Hardy inequalities in metric spaces in terms of Assouad (co)dimensions. Our sufficient conditions in the case where the complement is thin are new, even ...

• Weakly porous sets and Muckenhoupt Ap distance functions 

  Anderson, Theresa C.; Lehrbäck, Juha; Mudarra, Carlos; Vähäkangas, Antti V. (Elsevier, 2024)

  We examine the class of weakly porous sets in Euclidean spaces. As our first main result we show that the distance weight w(x)=dist(x,E)−α belongs to the Muckenhoupt class A1, for some α>0, if and only if E⊂Rn is weakly ...