Talk:Trudinger's theorem

Why $m$ used in statement of theorem?

I'm puzzled about the use of $m$ in the theorem. The problem is that nothing seems to depend on $m$. For example,

$A(t)=\exp \left(t^{n/(n-m)}\right)-1.$

becomes

$A(t)=\exp \left(t^{p/(p-1)}\right)-1.$

when you substitute $n=mp$. Then the imbedding

$W^{m,p}(\Omega )\hookrightarrow L_{A}(\Omega )$

exists for all $m$ according to the statement of the theorem as I understand it. Surely, if this is true, then there is a better way to state the theorem? -- KarlHallowell (talk) 04:38, 28 June 2009 (UTC)