Does the general Holder's inequality works also for $p,q,r\in (0,1)$?

Question

General Holder's inequality says that for $p,q\geq 1$ and for $r>0$ s.t. $\frac{1}{r}=\frac{1}{p}+\frac{1}{q}$ we have for $fg\in L^r$, $f\in L^p$ and $g\in L^q$ $$\|fg\|_r\leq \|f\|_p\|g\|_q.$$ But does it still hold if $p,q\in (0,1)$. For example, if $p=q=\frac{1}{2}$ and $r=\frac{1}{4}$ we have that $$\frac{1}{r}=\frac{1}{p}+\frac{1}{q},$$ but does $$\|fg\|_{L^{1/4}}\leq \|f\|_{L^{1/2}}\|g\|_{L^{1/2}}\ \ ?$$