H^{-1} norm

Let || u || denote the H^{-1}(Omega) norm of u. ((Here H^{-1}(Omega) is the dual of H_0^1(Omega) .))

Question: Does there exist some C>0 such that for all nice functions $u$ defined on $Omega$ we have

|| |u| || <= C || u || .


ie. Taking H^{-1} norm of the absolute value of u.


I have tried using the " representave" in H_0^1 promised by Riesz and some PDE theory, also I have tried using Fourier transform...

It seems like a really easy question but I can't prove either way.


thanks


craig
.

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