Is the following theorem true and if so does it have a name?
Theorem: Let $p$, $q$, $r\in\left(0, \infty\right]$ with $\frac{1}{q}=\frac{1}{p}+\frac{1}{r}$. Every $L^{q}$-function is the product of a $L^p$-function and a $L^{r}$-function.
I believe the statement is correct but I can't find the corresponding literature I need.