Reverse of Hausdorff Young Inequality

Question

The Hausdorff Young Inequality gives us that $$\|\hat f\|_{L^q(\mathbb{R}^n)} \leq \| f\|_{L^p(\mathbb{R}^n)}$$ if $1 \leq p \leq 2$ and $\frac{1}{q} + \frac{1}{p} = 1$, but does the converse also hold in general? Namely $$\|f\|_{L^q(\mathbb{R}^n)} \leq \| \hat f\|_{L^p(\mathbb{R}^n)}$$ for $1 \leq p \leq 2$ and $\frac{1}{q} + \frac{1}{p} = 1$? I am just confused on the dependence of the Fourier transform being less than the original function?