Assuming that a function g is such that $ g(x) \leq C ( 1 + |x|)^{(-1 - \varepsilon)}$ for some $\varepsilon > 0$ , then how can we prove that $ \sum_{n = - \infty}^{n = + \infty} | g(x- k - \frac{n}{2}) g(x- l - \frac{n}{2}) \leq C(1 + |k-l|)^{(-1 - \varepsilon)} $ for all $x \in [0,1]$ ?
Thank you for your help