If $f\in L^p(\mathbb{R}^d)$ and $g\in L^q(\mathbb{R}^d)$, with $1\leq p\leq \infty $ and $1/p+1/q=1$, show $f*g$ is uniformly continuous.
And if $1<p<\infty$, prove that $\lim_{|x|\rightarrow\infty}f*g(x)=0$.
I'm completely lost, please help. Maybe $||f*g||_{\infty}\leq||f||_p||g||_{q}$ will be usefull because the exercise also asks for it and I've already done.
The convolution is $f*g(x)=\int_{\mathbb{R}^d} f(x-y)g(y)dy$