Uma nova caracterização dos Espaços de Sobolev W^{1,p}(R^n) - Elias, Thaysa Fernanda (2018)
In this work we will present a new characterization of the Sobolev space W^{1,1}(\R^n) and also we give another proof of the characterization of the Sobolev space W^{1,p}(\R^n), 1<p<∞, in terms of Poincaré inequalities. Both characterization was proved by Piotr Hajlasz in the paper "A new characterization of the Sobolev spaces" published in the journal Studia Mathematica in 2003.