Georgian Math. J.

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

On the Continuity of the Nemytskij Operator between the Spaces $L^{p_{1}(x)}$ and $L^{p_{2}(x)}$

On the Continuity of the Nemytskij Operator between the Spaces
$L^{p_{1}(x)}$ and $L^{p_{2}(x)}$