The usual description of the Fourier transform (over)emphasizes the role of $L^p$-spaces. $L^1$ is used to define the Fourier integral and convolution, and
$L^2$ is needed to express the fact that the Fourier transform is a unitary mapping (over the torus, but also for the Euclidean space $R^d$). But the drawback it the asymmetry, which becomes apparent when proving the Fourier inversion theorem.

Time-frequency Analysis resp.\ {\it Gabor Analysis} suggest to take a more symmetric view on the time resp.\ frequency side of a function by taking a {\it time-frequency perspective}. In this context also the so-called Segal algbra $S_0$ and its dual play a significant role, e.g. in order to derive robustness results for Gabor expansions.

With $S_0$ being the smallest element in this family of isometrically time-frequency shift-invariant spaces (and correspondingly its dual space $S_0'$ being the largest one of its kind) it appears to be natural to study the whole family of such spaces, which we call {\it Fourier standard spaces}.

We will exploit the richness of this family of spaces, which includes aside of $L^p$-spaces also the Wiener amalgam spaces $W(L^p,\ell^q)$, the modulation spaces
$M^{p,q}$, the space of convolution kernels acting boundedly on $L^p$ and so on.
Nevertheless one can derive quite general results for the spaces in this family and show that this new perspective is quite useful, also from the point of view of classical analysis. For example one can characterize the reflexive spaces in this family or the ones which are dual spaces.