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)