High Quality Content by WIKIPEDIA articles! The Sobolev conjugate of p for 1leq p <n, where n is space dimensionality, is p^*=frac{pn}{n-p}>p This is an important parameter in the Sobolev inequalities. A question arises whether u from the Sobolev space W1,p(Rn) belongs to Lq(Rn) for some q>p. More specifically, when does |Du|_{L^p(R^n)} control |u|_{L^q(R^n)}? It is easy to check that the following inequality |u|_{L^q(R^n)}leq C(p,q)|Du|_{L^p(R^n)} (*)

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