I'm just asking if there is a name for the space of functions on $\mathbb R^n$ whose norm is defined by


$$ \|f\|=\|\hat f\|\_{L^p} $$


for $p\in [1,\infty]$. I find it handy to give it a name when discussing the success/failure of Young's inequality on the Fourier transform, among other things.



Is there a name for this space?
In the literature you can sometimes see them called **Fourier-Lebesgue** spaces, with notation $\mathcal{F} L^p(\mathbb{R}^n)$, consisting of the set of all tempered distributions whose norm (as you wrote) is finite. 


See, e.g., <http://arxiv.org/abs/0804.1730> and <http://arxiv.org/abs/0801.1444>


