I still stuck on a detail of a proof of van der corput inequality. Let $\left(x_1 , x_2 , ..., x_N\right) \in \mathbb{C^{N}}$ and $1 \leq H \leq N$ an integer. Let us consider the sum $\Sigma_{2} = \sum\limits_{p=1}^{N+H-1} \sum\limits_{\substack{r,s = 0 \\ r < s}}^{H-1} x_{p-r}.\overline{x_{p-s}} $. I am wondering why $\Sigma_{2} = \sum\limits_{h=1}^{H-1} (H-h) \sum\limits_{n=1}^{N} x_n.\overline{x_{n+h}}$.
Thanks in advance !