The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (919 KB) | Metadata | Table of Contents | ZAA summary
Volume 16, Issue 2, 1997, pp. 377–386
DOI: 10.4171/ZAA/768

Published online: 1997-06-30

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

Cheng Chur-jen[1] and Martin Väth[2]

(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