On the $\mathcal L$-Characteristic of the Superposition Operator in Lebesgue Spaces with Mixed Norm

Cheng Chur-jen; Martin Väth

doi:10.4171/zaa/768

JournalszaaVol. 16, No. 2pp. 377–386

On the $L$ -Characteristic of the Superposition Operator in Lebesgue Spaces with Mixed Norm

Cheng Chur-jen
Tunhai University, Taichung, Taiwan
Martin Väth
Czech Academy of Sciences, Prague, Czech Republic

$On the $\mathcal L$-Characteristic of the Superposition Operator in Lebesgue Spaces with Mixed Norm cover$

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Abstract

We consider the superposition operator $F x (t, s) = f (t, s, x (t, s))$ 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 $L$ -characteristic of $F$ . We also prove some theorems, which imply that $F$ is uniformly continuous on balls in the interior of its $L$ -characteristic.

Cite this article

Cheng Chur-jen, Martin Väth, On the $L$ -Characteristic of the Superposition Operator in Lebesgue Spaces with Mixed Norm. Z. Anal. Anwend. 16 (1997), no. 2, pp. 377–386

DOI 10.4171/ZAA/768