Let f$\displaystyle $\f \in {L^4}\left( R \right),g \in {L^5}\left( R \right)\$ . Check the following:

1)$\displaystyle fg$\fg \in {L^{20/9}}(R)\$$

2) $\displaystyle $\[fg \notin {L^6}\left( R \right)\]$$

Where

$\displaystyle $\L^P} \buildrel \Delta \over = \left\{ {f:I \to R/f Lebesgue int} \right\}\$

Thanks...