The spaces $L^p$ with $0<p<1$

Question

Assume that there exists a constant $ M> 0$ such that $/\hat{u}/ >M$ .

Is the following inequality true?

$\left \| \hat{u}\right \|_{L^{p}} $ $\leq $ $\left \| \hat{u}\right \|_{L^{2}} $ with $ 0<p<1$ .

Thanks.