What do these symbols $C^1_0(\mathbb{R}^n)$ and $C^1(\mathbb{R}^n)$ mean?

Question

The symbols $C^1_0(\mathbb{R}^n)$ and $C^1(\mathbb{R}^n)$ appear in this context, but I don't know the meaning of them.

Let $f$ be integrable on $\mathbb{R}^n$ and $g\in C^1_0(\mathbb{R}^n).$ Then, prove that $\displaystyle\int_{\mathbb{R}^n} f(y)g(x-y) dy\in C^1(\mathbb{R}^n).$

What do $C^1_0(\mathbb{R}^n)$ and $C^1(\mathbb{R}^n)$ mean ?