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High Quality Content by WIKIPEDIA articles! In mathematics, there is in mathematical analysis a class of Sobolev inequalities, relating norms including those of Sobolev spaces. These are used to prove the Sobolev embedding theorem, giving inclusions between certain Sobolev spaces, and the Kondrashov theorem (or Rellich-Kondrashov theorem) showing that under slightly stronger conditions some Sobolev spaces are compactly embedded in others. They are named after Sergei Lvovich Sobolev.Let Wk,p(Rn) denote the Sobolev space consisting of all real-valued functions on Rn whose first k weak derivatives are functions in Lp.