Estimation of Convolution

[FreiesMathe]

Hello, we had a task and solved it, but we aren't sure if it's correct like this. It'd be great if someone could help us c:

Given two functions $\displaystyle f,g \in L^2(\mathbb{R}^d)$. Is the following estimation correct?

$\displaystyle (f*g)(x) = \int_{\mathbb{R}^d} f(x-y)g(y) \, \mathrm{d}y = \text{||} fg \text{||}_1 \le \text{||} f \text{||}_2 \text{||} g \text{||}_2$

We used Hölder's inequality for this.
Thanks for your help