  It is shown that two conditions $f(a + \cdot) - f(\cdot) \in L^p(R)$, and
$(\sin b \cdot) f(\cdot) \in L^p(R)$ guarantee $f \in L^p(R)$, $1 \leq p <
\infty$, if and only if $ab$ is not in $(\pi Z)$.
