Showing items with similar title or keywords.

• Uniform rectifiability and ε-approximability of harmonic functions in Lp 

  Hofmann, Steve; Tapiola, Olli (Centre Mersenne; l'Institut Fourier,, 2020)

  Suppose that E⊂Rn+1 is a uniformly rectifiable set of codimension 1. We show that every harmonic function is ε-approximable in Lp(Ω) for every p∈(1,∞), where Ω:=Rn+1∖E. Together with results of many authors this shows that ...

• Uniform rectifiability implies Varopoulos extensions 

  Hofmann, Steve; Tapiola, Olli (Elsevier, 2021)

  We construct extensions of Varopolous type for functions f∈BMO(E), for any uniformly rectifiable set E of codimension one. More precisely, let Ω⊂Rn+1 be an open set satisfying the corkscrew condition, with an n-dimensional ...

• A proof of Carleson's 𝜀2-conjecture 

  Jaye, Benjamin; Tolsa, Xavier; Villa, Michele (Mathematics Department, Princeton University, 2021)

  In this paper we provide a proof of the Carleson 𝜀2-conjecture. This result yields a characterization (up to exceptional sets of zero length) of the tangent points of a Jordan curve in terms of the finiteness of the ...

• Gradient estimates for heat kernels and harmonic functions 

  Coulhon, Thierry; Jiang, Renjin; Koskela, Pekka; Sikora, Adam (Elsevier, 2020)

  Let (X,d,μ) be a doubling metric measure space endowed with a Dirichlet form E deriving from a “carré du champ”. Assume that (X,d,μ,E) supports a scale-invariant L2-Poincaré inequality. In this article, we study the following ...

• 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 ...