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If $f\in H^2(\mathbb R^2)$, I want to show that

$||f||_{L^\infty}\le c||f||_{H^1} [1+\ln(1+||f||_{H^2})]$

How can I get the "ln"? and how can I make it into a product of $H^1$ and $H^2$ norm?

It is actually one of my Real variables's project. So how can I do this inequality in an relativly "elementary" way?

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    I have not tried this myself, but you could try to use the Fourier transform.2012-12-21

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