JournalszaaVol. 16, No. 2pp. 377–386

On the L\mathcal 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 Fx(t,s)=f(t,s,x(t,s))Fx(t,s) = f(t,s,x(t,s)) of functions of two variables in spaces with mixed norm [LpLq][L_p \to L_q]. After establishing a necessary and sufficient acting condition, we get some conclusions on the L\mathcal L-characteristic of FF. We also prove some theorems, which imply that FF is uniformly continuous on balls in the interior of its L\mathcal L-characteristic.

Cite this article

Cheng Chur-jen, Martin Väth, On the L\mathcal 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