Sobolev space
Write formula_214 for the Sobolev space of some compact Riemannian manifold of dimension "n". Here "k" can be any real number, and 1 ≤ "p" ≤ ∞. (For "p" = ∞ the Sobolev space formula_61 is defined to be the Hölder space "C""n",α where "k" = "n" + α and 0 &lt; α ≤ 1.) The Sobolev embedding theorem states that if formula_216 and formula_217 then