If $f, g$ are two functions on a bounded subset of $\mathbb R$, is there a bound on $\|f-g\|_2$, involving only $\|f-g\|_1$, $\|g\|_2$, and some other finite quantities? Here, $\|\cdot\|_p$ is the $L^p$-norm.
Thanks!
If $f, g$ are two functions on a bounded subset of $\mathbb R$, is there a bound on $\|f-g\|_2$, involving only $\|f-g\|_1$, $\|g\|_2$, and some other finite quantities? Here, $\|\cdot\|_p$ is the $L^p$-norm.
Thanks!