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High Quality Content by WIKIPEDIA articles! The Sobolev conjugate of p for 1leq 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 qp. 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)} ( )