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A new characterization of the Sobolev space

Studia Mathematica (2003) 159(2) 263-275
DOI: 10.4064/sm159-2-7
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Abstract

The purpose of this paper is to provide a new characterization of the Sobolev space W1,1 (ℝn). We also show a new proof of the characterization of the Sobolev space W1,p(ℝn), 1 ≤ p < ∞, in terms of Poincaré inequalities.

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Hajłasz, P. (2003). A new characterization of the Sobolev space. Studia Mathematica, 159(2), 263–275. https://doi.org/10.4064/sm159-2-7

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