Reference Request: Hausdorff–Young inequality for the inverse Fourier seires

Let $ \hat f : \mathbb Z^d \to \mathbb C $ denote a function in $\ell^p(\mathbb Z^d)$ where $p \in [1,2]$.Let $f : \mathbb T^d = (\mathbb R / 2\pi \mathbb Z)^d \to \mathbb C$ denote the inverse Fourier transform/series of $\hat f$.Let $p'$ satisfy $\frac 1 p + \frac 1 {p'} = 1$.I am looking for a reference for the inequality $$ || f ||_{L^{p'}(\mathbb T^d) } \le || \hat f ||_{\ell^p(\mathbb Z^d) } .$$The proof should be an application of the Riesz-Thorin theorem. Does anyone know a proof written down somewhere?