Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1997-06-30
On the $\mathcal L$-Characteristic of the Superposition Operator in Lebesgue Spaces with Mixed NormCheng Chur-jen and Martin Väth (1) Tunhai University, Taichung, Taiwan
(2) Czech Academy of Sciences, Prague, Czech Republic
We consider the superposition operator $Fx(t,s) = f(t,s,x(t,s))$ of functions of two variables in spaces with mixed norm $[L_p \to L_q]$. After establishing a necessary and sufficient acting condition, we get some conclusions on the $\mathcal L$-characteristic of $F$. We also prove some theorems, which imply that $F$ is uniformly continuous on balls in the interior of its $\mathcal L$-characteristic.
Keywords: Superposition operators, spaces with mixed norm, $\mathcal L$-characteristics
Chur-jen Cheng, Väth Martin: On the $\mathcal L$-Characteristic of the Superposition Operator in Lebesgue Spaces with Mixed Norm. Z. Anal. Anwend. 16 (1997), 377-386. doi: 10.4171/ZAA/768