I have read that if we have a weighted projective space $\mathbb{P}$ in general it is not true that: $$ \mathcal{O}_\mathbb{P}(n)\otimes \mathcal{O}_\mathbb{P}(m)\simeq \mathcal{O}_\mathbb{P}(n+m). $$
Now, this is the case if $\mathbb{P}$ is just a regular projective space $\mathbb{P}^r$. Is there any result that says when this is true? Does it depend on whether the sheaves $\mathcal{O}_\mathbb{P}(n), \mathcal{O}_\mathbb{P}(m)$ are invertible or not? What happens in easy cases like $\mathbb{P}(1,\ldots, 1,a)$?