# Is there a Hausdorff-Young inequality which applies between a length n sequence and its n Discrete Fourier Transform?

I have been looking around for generalization of the Hausdorff-Young inequality that can be applied between a length $n$ sequence and its $n$-Discrete Fourier Transform (DFT) but no luck.
The n-DFT $X$ of a sequence $x$ of length $n$ is defined as: $$X_k = \sum\limits_{l=0}^{n-1} x_l \exp\left(\frac{-2\pi j k l}{ n}\right)$$ Any help is appreciated.
Regard.