**Marek Galewski**

## On the Continuity of the Nemytskij Operator
between the Spaces

$L^{p_{1}(x)}$ and $L^{p_{2}(x)}$

**Abstract:**

We provide a generalized sufficient condition for the continuity of the
Nemytskij operator between $L^{p_{1}\left( x\right) \text{ }}$ and
$L^{p_{2}\left( x\right) }$. An example is given.

**Keywords:**

Nemytskij operator, continuity, $L^p(x)$-space, generalized growth conditions.

**MSC 2000:** 58C07, 46T99